Finite Group Databasebeta

← Group #13048672

Character table — Group #13048672

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11111122222222233333344466666666666666666661212121212121212121212121212121218181818181818181818181818181818181818181818363636363636545454545454
order1233663334666121244121212121212122333366666612121212121212123333666612121212121212124466666666121212121212121212121212121212121212226666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-1-1-1-1-1-1111-11111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111-1-1-1-1-1-1111-11111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-11-111-1-1
χ6111111111-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-11-1-111
χ7111111111-1111-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-111
χ8111111111-1111-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1
χ922222222222222222222222222-1-1-1222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10022-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ102222222222222222222222222-12-1-122-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-100-1-122-1-1-1-10000-1-122-1-1-1-1000000000000
χ112222222222222222222222222-1-12-122-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-100-1-1-1-122-1-10000-1-1-1-122-1-1000000000000
χ122222222222222222222222222-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-12200-1-1-1-1-1-1220000-1-1-1-1-1-122000000000000
χ13222222222222222-2-2-2-2-2-2222-22-1-1-1-2-22-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-100-2-21111110000-2-2111111000000000000
χ14222222222222222-2-2-2-2-2-2222-2-12-1-1-2-2-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-10011-2-21111000011-2-21111000000000000
χ15222222222222222-2-2-2-2-2-2222-2-1-12-1-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1001111-2-21100001111-2-211000000000000
χ16222222222222222-2-2-2-2-2-2222-2-1-1-12-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-12200111111-2-20000111111-2-2000000000000
χ17222222222-2222-2-2222222-2-2-2-22-1-1-1-2-22-1-1-1-2-21111112-1-1-12-1-1-1-2-211111100-2-2111111000022-1-1-1-1-1-1000000000000
χ18222222222-2222-2-2222222-2-2-2-2-12-1-1-2-2-12-1-111-2-21111-12-1-1-12-1-111-2-211110011-2-211110000-1-122-1-1-1-1000000000000
χ19222222222-2222-2-2222222-2-2-2-2-1-12-1-2-2-1-12-11111-2-211-1-12-1-1-12-11111-2-211001111-2-2110000-1-1-1-122-1-1000000000000
χ20222222222-2222-2-2222222-2-2-2-2-1-1-12-2-2-1-1-12111111-2-2-1-1-12-1-1-12111111-2-200111111-2-20000-1-1-1-1-1-122000000000000
χ21222222222-2222-2-2-2-2-2-2-2-2-2-2-222-1-1-1222-1-1-1-2-21111112-1-1-12-1-1-1-2-21111110022-1-1-1-1-1-10000-2-2111111000000000000
χ22222222222-2222-2-2-2-2-2-2-2-2-2-2-22-12-1-122-12-1-111-2-21111-12-1-1-12-1-111-2-2111100-1-122-1-1-1-1000011-2-21111000000000000
χ23222222222-2222-2-2-2-2-2-2-2-2-2-2-22-1-12-122-1-12-11111-2-211-1-12-1-1-12-11111-2-21100-1-1-1-122-1-100001111-2-211000000000000
χ24222222222-2222-2-2-2-2-2-2-2-2-2-2-22-1-1-1222-1-1-12111111-2-2-1-1-12-1-1-12111111-2-200-1-1-1-1-1-1220000111111-2-2000000000000
χ25222222-1-1-12-1-1-122000000-1-1-10222200222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200000000222200000000-1-1-1-1-1-1000000
χ26222222-1-1-12-1-1-122000000-1-1-10222200222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000-2-2-2-200000000111111000000
χ27222222-1-1-1-2-1-1-1-2-200000011102222002222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111112-20000000022-2-200000000-1-1-1111000000
χ28222222-1-1-1-2-1-1-1-2-200000011102222002222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2200000000-2-22200000000111-1-1-1000000
χ292-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000222200-2-2-2-2000000002222-2-2-2-200000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ302-222-2-22220-2-2-2002i−2i2i2i−2i−2i00002-1-1-100-2111003−33−33−32-1-1-1-2111003−33−33−30000−i3i3−i3i3−i3i300002i−2i−ii−ii−ii000000000000
χ312-222-2-22220-2-2-2002i−2i2i2i−2i−2i00002-1-1-100-211100−33−33−332-1-1-1-211100−33−33−330000i3−i3i3−i3i3−i300002i−2i−ii−ii−ii000000000000
χ322-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-12-1-1001-2113−3003−3−33-12-1-11-2113−3003−3−3300−i3i300−i3i3i3−i30000−ii2i−2i−ii−ii000000000000
χ332-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-12-1-1001-211−3300−333−3-12-1-11-211−3300−333−300i3−i300i3−i3−i3i30000−ii2i−2i−ii−ii000000000000
χ342-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-1-12-10011-213−3−33003−3-1-12-111-213−3−33003−300−i3i3i3−i300−i3i30000−ii−ii2i−2i−ii000000000000
χ352-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-1-12-10011-21−333−300−33-1-12-111-21−333−300−3300i3−i3−i3i300i3−i30000−ii−ii2i−2i−ii000000000000
χ362-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-1-1-1200111-23−33−3−3300-1-1-12111-23−33−3−330000−i3i3−i3i3i3−i3000000−ii−ii−ii2i−2i000000000000
χ372-222-2-22220-2-2-2002i−2i2i2i−2i−2i0000-1-1-1200111-2−33−333−300-1-1-12111-2−33−333−30000i3−i3i3−i3−i3i3000000−ii−ii−ii2i−2i000000000000
χ382-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000222200-2-2-2-2000000002222-2-2-2-20000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392-222-2-22220-2-2-200−2i2i−2i−2i2i2i00002-1-1-100-2111003−33−33−32-1-1-1-2111003−33−33−30000i3−i3i3−i3i3−i30000−2i2ii−ii−ii−i000000000000
χ402-222-2-22220-2-2-200−2i2i−2i−2i2i2i00002-1-1-100-211100−33−33−332-1-1-1-211100−33−33−330000−i3i3−i3i3−i3i30000−2i2ii−ii−ii−i000000000000
χ412-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-12-1-1001-2113−3003−3−33-12-1-11-2113−3003−3−3300i3−i300i3−i3−i3i30000i−i−2i2ii−ii−i000000000000
χ422-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-12-1-1001-211−3300−333−3-12-1-11-211−3300−333−300−i3i300−i3i3i3−i30000i−i−2i2ii−ii−i000000000000
χ432-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-1-12-10011-213−3−33003−3-1-12-111-213−3−33003−300i3−i3−i3i300i3−i30000i−ii−i−2i2ii−i000000000000
χ442-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-1-12-10011-21−333−300−33-1-12-111-21−333−300−3300−i3i3i3−i300−i3i30000i−ii−i−2i2ii−i000000000000
χ452-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-1-1-1200111-23−33−3−3300-1-1-12111-23−33−3−330000i3−i3i3−i3−i3i3000000i−ii−ii−i−2i2i000000000000
χ462-222-2-22220-2-2-200−2i2i−2i−2i2i2i0000-1-1-1200111-2−33−333−300-1-1-12111-2−33−333−30000−i3i3−i3i3i3−i3000000i−ii−ii−i−2i2i000000000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3230000−3−3i32−3+3i3200000000000000000000000000001100000000−1−i32−1+i32−1−i32−1+i32000000001−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3230000−3−3i32−3+3i320000000000000000000000000000-1-1000000001+i321−i321+i321−i3200000000-11+i321−i32-11+i321−i32-1-11+i321−i321+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323−3−3i32−3+3i32-300003+3i323−3i3200000000000000000000000000001100000000−1−i32−1+i32−1−i32−1+i32000000001−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323−3−3i32−3+3i32-300003+3i323−3i320000000000000000000000000000-1-1000000001+i321−i321+i321−i3200000000-11+i321−i32-11+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33−3−3i32−3+3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-300003+3i323−3i3200000000000000000000000000001-100000000−1−i32−1+i321+i321−i32000000001−1−i32−1+i32-11+i321−i321-1−1−i32−1+i321+i321−i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33−3−3i32−3+3i323+3i323−3i3233−3−3i32−3+3i32−3−3i32−3+3i32-33+3i323−3i32-300003+3i323−3i320000000000000000000000000000-11000000001+i321−i32−1−i32−1+i3200000000-11+i321−i321−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33−3−3i32−3+3i323+3i323−3i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i3230000−3−3i32−3+3i3200000000000000000000000000001-100000000−1−i32−1+i321+i321−i32000000001−1−i32−1+i32-11+i321−i32-111+i321−i32−1−i32−1+i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i323−3−3i32−3+3i32-33−3−3i32−3+3i323+3i323−3i32-3-33+3i323−3i323+3i323−3i32-33+3i323−3i3230000−3−3i32−3+3i320000000000000000000000000000-11000000001+i321−i32−1−i32−1+i3200000000-11+i321−i321−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3230000−3+3i32−3−3i3200000000000000000000000000001100000000−1+i32−1−i32−1+i32−1−i32000000001−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3230000−3+3i32−3−3i320000000000000000000000000000-1-1000000001−i321+i321−i321+i3200000000-11−i321+i32-11−i321+i32-1-11−i321+i321−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323−3+3i32−3−3i32-300003−3i323+3i3200000000000000000000000000001100000000−1+i32−1−i32−1+i32−1−i32000000001−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i32
χ5833−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323−3+3i32−3−3i32-300003−3i323+3i320000000000000000000000000000-1-1000000001−i321+i321−i321+i3200000000-11−i321+i32-11−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3+3i32−3−3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-300003−3i323+3i3200000000000000000000000000001-100000000−1+i32−1−i321−i321+i32000000001−1+i32−1−i32-11−i321+i321-1−1+i32−1−i321−i321+i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3+3i32−3−3i323−3i323+3i3233−3+3i32−3−3i32−3+3i32−3−3i32-33−3i323+3i32-300003−3i323+3i320000000000000000000000000000-11000000001−i321+i32−1+i32−1−i3200000000-11−i321+i321−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3+3i32−3−3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i3230000−3+3i32−3−3i3200000000000000000000000000001-100000000−1+i32−1−i321−i321+i32000000001−1+i32−1−i32-11−i321+i32-111−i321+i32−1+i32−1−i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i323−3+3i32−3−3i32-33−3+3i32−3−3i323−3i323+3i32-3-33−3i323+3i323−3i323+3i32-33−3i323+3i3230000−3+3i32−3−3i320000000000000000000000000000-11000000001−i321+i32−1+i32−1−i3200000000-11−i321+i321−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ63444444-2-2-24-2-2-244000000-2-2-204-2-2-2004-2-2-244-2-2-2-2-2-2-2111-2111-2-21111110000000000000000000000000000000000
χ64444444-2-2-24-2-2-244000000-2-2-20-24-2-200-24-2-2-2-244-2-2-2-21-2111-21111-2-211110000000000000000000000000000000000
χ65444444-2-2-24-2-2-244000000-2-2-20-2-24-200-2-24-2-2-2-2-244-2-211-2111-211111-2-2110000000000000000000000000000000000
χ66444444-2-2-24-2-2-244000000-2-2-20-2-2-2400-2-2-24-2-2-2-2-2-244111-2111-2111111-2-20000000000000000000000000000000000
χ67444444-2-2-2-4-2-2-2-4-400000022204-2-2-2004-2-2-2-4-4222222-2111-211122-1-1-1-1-1-10000000000000000000000000000000000
χ68444444-2-2-2-4-2-2-2-4-40000002220-24-2-200-24-2-222-4-422221-2111-211-1-122-1-1-1-10000000000000000000000000000000000
χ69444444-2-2-2-4-2-2-2-4-40000002220-2-24-200-2-24-22222-4-42211-2111-21-1-1-1-122-1-10000000000000000000000000000000000
χ70444444-2-2-2-4-2-2-2-4-40000002220-2-2-2400-2-2-24222222-4-4111-2111-2-1-1-1-1-1-1220000000000000000000000000000000000
χ714-444-4-4-2-2-20222000000000000444400-4-4-4-400000000-2-2-2-22222000000000000000000000000000000000000000000
χ724-444-4-4-2-2-202220000000000004-2-2-200-42220023−2323−2323−23-21112-1-1-100−33−33−330000000000000000000000000000000000
χ734-444-4-4-2-2-202220000000000004-2-2-200-422200−2323−2323−2323-21112-1-1-1003−33−33−30000000000000000000000000000000000
χ744-444-4-4-2-2-20222000000000000-24-2-2002-42223−230023−23−23231-211-12-1-1−3300−333−30000000000000000000000000000000000
χ754-444-4-4-2-2-20222000000000000-24-2-2002-422−232300−232323−231-211-12-1-13−3003−3−330000000000000000000000000000000000
χ764-444-4-4-2-2-20222000000000000-2-24-20022-4223−23−23230023−2311-21-1-12-1−333−300−330000000000000000000000000000000000
χ774-444-4-4-2-2-20222000000000000-2-24-20022-42−232323−2300−232311-21-1-12-13−3−33003−30000000000000000000000000000000000
χ784-444-4-4-2-2-20222000000000000-2-2-2400222-423−2323−23−232300111-2-1-1-12−33−333−3000000000000000000000000000000000000
χ794-444-4-4-2-2-20222000000000000-2-2-2400222-4−2323−232323−2300111-2-1-1-123−33−3−33000000000000000000000000000000000000
χ8066−3−3i3−3+3i3−3−3i3−3+3i3-33+3i323−3i326-33+3i323−3i32−3−3i3−3+3i3000000-33+3i323−3i32000000000000000000000000000000000002200000000−1−i3−1+i3−1−i3−1+i300000000-11+i321−i32-11+i321−i32000000
χ8166−3−3i3−3+3i3−3−3i3−3+3i3-33+3i323−3i326-33+3i323−3i32−3−3i3−3+3i3000000-33+3i323−3i3200000000000000000000000000000000000-2-2000000001+i31−i31+i31−i3000000001−1−i32−1+i321−1−i32−1+i32000000
χ8266−3−3i3−3+3i3−3−3i3−3+3i3-33+3i323−3i32-6-33+3i323−3i323+3i33−3i30000003−3−3i32−3+3i32000000000000000000000000000000000002-200000000−1−i3−1+i31+i31−i300000000-11+i321−i321−1−i32−1+i32000000
χ8366−3−3i3−3+3i3−3−3i3−3+3i3-33+3i323−3i32-6-33+3i323−3i323+3i33−3i30000003−3−3i32−3+3i3200000000000000000000000000000000000-22000000001+i31−i3−1−i3−1+i3000000001−1−i32−1+i32-11+i321−i32000000
χ8466−3+3i3−3−3i3−3+3i3−3−3i3-33−3i323+3i326-33−3i323+3i32−3+3i3−3−3i3000000-33−3i323+3i32000000000000000000000000000000000002200000000−1+i3−1−i3−1+i3−1−i300000000-11−i321+i32-11−i321+i32000000
χ8566−3+3i3−3−3i3−3+3i3−3−3i3-33−3i323+3i326-33−3i323+3i32−3+3i3−3−3i3000000-33−3i323+3i3200000000000000000000000000000000000-2-2000000001−i31+i31−i31+i3000000001−1+i32−1−i321−1+i32−1−i32000000
χ8666−3+3i3−3−3i3−3+3i3−3−3i3-33−3i323+3i32-6-33−3i323+3i323−3i33+3i30000003−3+3i32−3−3i32000000000000000000000000000000000002-200000000−1+i3−1−i31−i31+i300000000-11−i321+i321−1+i32−1−i32000000
χ8766−3+3i3−3−3i3−3+3i3−3−3i3-33−3i323+3i32-6-33−3i323+3i323−3i33+3i30000003−3+3i32−3−3i3200000000000000000000000000000000000-22000000001−i31+i3−1+i3−1−i3000000001−1+i32−1−i32-11−i321+i32000000
χ886-6−3−3i3−3+3i33+3i33−3i36−3−3i3−3+3i30-63+3i33−3i3006i−6i6ζ116ζ7−6ζ11−6ζ7000000000000000000000000000000000000000000000000000000000000000000000000
χ896-6−3−3i3−3+3i33+3i33−3i36−3−3i3−3+3i30-63+3i33−3i300−6i6i−6ζ11−6ζ76ζ116ζ7000000000000000000000000000000000000000000000000000000000000000000000000
χ906-6−3+3i3−3−3i33−3i33+3i36−3+3i3−3−3i30-63−3i33+3i3006i−6i6ζ76ζ11−6ζ7−6ζ11000000000000000000000000000000000000000000000000000000000000000000000000
χ916-6−3+3i3−3−3i33−3i33+3i36−3+3i3−3−3i30-63−3i33+3i300−6i6i−6ζ7−6ζ116ζ76ζ11000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-12−6−6i3−6+6i36+6i36−6i3-63+3i33−3i306−3−3i3−3+3i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-12−6+6i3−6−6i36−6i36+6i3-63−3i33+3i306−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.