Finite Group Databasebeta

← Group #13167438

Character table — Group #13167438

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order12442346121233666661212121212121233666666612121212121212121222442466888888881212444468888121212121212121212242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-1-111-1-1-1-1-111111111-1-1-1-1-1-111
χ71111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-111
χ81111-11-111111-1-1-111-1-1-1111111-1-1-1-1-111-11111-1-1-1-11111-1-111-1-1-1-1111111-1-111-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-111ii−i−iii−i−i-1-11-11-11i−ii−i-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1011-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-111ii−i−iii−i−i-1-1-11-111−ii−ii-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ1111-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-111−i−iii−i−iii-1-11-11-11−ii−ii-111-1-111-1-1−i−iii−i−iii−ii−ii
χ1211-1-111-11-1-11111111-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-11-111−i−iii−i−iii-1-1-11-111i−ii−i-1-1-111-1-111−i−iii−i−iiii−ii−i
χ1311-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1111ii−i−i−i−iii-1-11-1-11-1i−i−ii111-1-1-1-111ii−i−i−i−iiii−i−ii
χ1411-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1111ii−i−i−i−iii-1-1-111-1-1−iii−i1-1-11111-1-1ii−i−i−i−iii−iii−i
χ1511-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1111−i−iiiii−i−i-1-11-1-11-1−iii−i111-1-1-1-111−i−iiiii−i−i−iii−i
χ1611-1-1-1111-1-111-1-1-111111-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1111−i−iiiii−i−i-1-1-111-1-1i−i−ii1-1-11111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000-2-20000-20000-200000000000000000000
χ1822222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1222222-1-100000000-1-12222-10000-1-1-1-1-1-1-1-1-1000000000000
χ1922222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1222222-1-100000000-1-1-2-2-2-2-10000-111111111000000000000
χ2022222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2-2-211000000001100001000013−33−33−33−3000000000000
χ2122222-12-1-1-122-12222-1222222-1-12-1-1-1-1-1-12-1-1-1-1-1-1-1-1-2-2-2-2-2-21100000000110000100001−33−33−33−33000000000000
χ222222-22-222222-2-2-222-2-2-2222222-2-2-2-2-222-22222-2-2-2-2-2-2-2-222-2-200000000-2-2000020000200000000000000000000
χ232222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-111112222-2-2-1-100000000-1-122-2-2100001-1-1-1-11111000000000000
χ242222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-111112222-2-2-1-100000000-1-1-2-2221000011111-1-1-1-1000000000000
χ252222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-11111-2-2-2-2221100000000110000-10000-13−33−3−33−33000000000000
χ262222-2-1-2-1-1-1221-2-2221-2-22222-1-1-21111-1-1-2-1-1-1-11111-2-2-2-2221100000000110000-10000-1−33−333−33−3000000000000
χ2722-2-222-22-2-22222222-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-222-22-2-200000000220000-20000200000000000000000000
χ2822-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-22-2-1-100000000112-22-2-100001-1-111-1-111000000000000
χ2922-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-21111111122-2-22-2-1-10000000011-22-22-10000111-1-111-1-1000000000000
χ3022-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-222-221100000000-1-1000010000-13−3−333−3−33000000000000
χ3122-2-22-1-2-11122-122221-2-2-2-2-2-2-1-12-1-1-1-1-1-1-211111111-2-222-221100000000-1-1000010000-1−333−3−333−3000000000000
χ3222-2-2-2222-2-222-2-2-222222-2-2-2-222-2-2-2-2-2222-2-2-2-22222-2-2222-2-2-20000000022000020000-200000000000000000000
χ3322-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-122-2-2-22-1-100000000112-2-2210000-1-1-11111-1-1000000000000
χ3422-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-122-2-2-22-1-10000000011-222-210000-111-1-1-1-111000000000000
χ3522-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-1-2-2222-21100000000-1-10000-1000013−3−33−333−3000000000000
χ3622-2-2-2-12-111221-2-222-122-2-2-2-2-1-1-21111-1-121111-1-1-1-1-2-2222-21100000000-1-10000-100001−333−33−3−33000000000000
χ372-22i−2i020-22i−2i22000-2-20002i2i−2i−2i2200000-2-202i2i−2i−2i00002-22i−2i002-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ382-22i−2i020-22i−2i22000-2-20002i2i−2i−2i2200000-2-202i2i−2i−2i00002-22i−2i002-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ392-22i−2i020-22i−2i22000-2-20002i2i−2i−2i2200000-2-202i2i−2i−2i0000-22−2i2i00-222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ402-22i−2i020-22i−2i22000-2-20002i2i−2i−2i2200000-2-202i2i−2i−2i0000-22−2i2i00-22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ412-2−2i2i020-2−2i2i22000-2-2000−2i−2i2i2i2200000-2-20−2i−2i2i2i00002-2−2i2i002-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ422-2−2i2i020-2−2i2i22000-2-2000−2i−2i2i2i2200000-2-20−2i−2i2i2i00002-2−2i2i002-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ432-2−2i2i020-2−2i2i22000-2-2000−2i−2i2i2i2200000-2-20−2i−2i2i2i0000-222i−2i00-22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ442-2−2i2i020-2−2i2i22000-2-2000−2i−2i2i2i2200000-2-20−2i−2i2i2i0000-222i−2i00-222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i0000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ4544444444441-24111-24111-21-21-2-211-2-21-2-21-21-211-2-2000000002222222200000000000000000000-1-1-1-1-1-1-1-10000
χ4644444444441-24111-24111-21-21-2-211-2-21-2-21-21-211-2-200000000-2-2-2-2-2-2-2-200000000000000000000111111110000
χ474444444444-214-2-2-214-2-2-21-21-211-2-211-211-21-21-2-21100000000000000000000000222200000000000000000-1-1-1-1
χ484444444444-214-2-2-214-2-2-21-21-211-2-211-211-21-21-2-21100000000000000000000000-2-2-2-2000000000000000001111
χ494444-44-44441-2-4-1-11-2-4-1-11-21-21-22-1-1221-221-21-2-1-122000000002222-2-2-2-200000000000000000000-1-1-1-111110000
χ504444-44-44441-2-4-1-11-2-4-1-11-21-21-22-1-1221-221-21-2-1-12200000000-2-2-2-22222000000000000000000001111-1-1-1-10000
χ514444-44-4444-21-422-21-422-21-21-21-122-1-1-21-1-21-2122-1-10000000000000000000000022-2-200000000000000000-1-111
χ524444-44-4444-21-422-21-422-21-21-21-122-1-1-21-1-21-2122-1-100000000000000000000000-2-2220000000000000000011-1-1
χ5344-4-444-44-4-41-24111-2-4-1-1-12-121-2-211-2-21-22-12-12-1-122000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−i−iii−i−iii0000
χ5444-4-444-44-4-41-24111-2-4-1-1-12-121-2-211-2-21-22-12-12-1-12200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000ii−i−iii−i−i0000
χ5544-4-444-44-4-4-214-2-2-21-4222-12-1-211-2-211-21-12-12-122-1-1000000000000000000000002i−2i2i−2i00000000000000000−ii−ii
χ5644-4-444-44-4-4-214-2-2-21-4222-12-1-211-2-211-21-12-12-122-1-100000000000000000000000−2i2i−2i2i00000000000000000i−ii−i
χ5744-4-4-4444-4-41-2-4-1-11-2411-12-121-22-1-1221-2-2-12-1211-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000−i−iiiii−i−i0000
χ5844-4-4-4444-4-41-2-4-1-11-2411-12-121-22-1-1221-2-2-12-1211-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000ii−i−i−i−iii0000
χ5944-4-4-4444-4-4-21-422-214-2-22-12-1-21-122-1-1-2112-12-1-2-211000000000000000000000002i−2i−2i2i00000000000000000−iii−i
χ6044-4-4-4444-4-4-21-422-214-2-22-12-1-21-122-1-1-2112-12-1-2-21100000000000000000000000−2i2i2i−2i00000000000000000i−i−ii
χ614-44i−4i040-44i−4i1-203-3-1203i−3ii−2i−i2i1-203-300-120i−2i−i2i3i−3i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ624-44i−4i040-44i−4i1-203-3-1203i−3ii−2i−i2i1-203-300-120i−2i−i2i3i−3i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ634-44i−4i040-44i−4i1-20-33-120−3i3ii−2i−i2i1-20-3300-120i−2i−i2i−3i3i00000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000
χ644-44i−4i040-44i−4i1-20-33-120−3i3ii−2i−i2i1-20-3300-120i−2i−i2i−3i3i0000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000
χ654-44i−4i0-202−2i2i44000-4-40004i4i−4i−4i-2-200000220−2i−2i2i2i00004-44i−4i00-2200000000−2i2i000000000000000000000000000000
χ664-44i−4i0-202−2i2i44000-4-40004i4i−4i−4i-2-200000220−2i−2i2i2i0000-44−4i4i002-2000000002i−2i000000000000000000000000000000
χ674-4−4i4i040-4−4i4i1-203-3-120−3i3i−i2ii−2i1-203-300-120−i2ii−2i−3i3i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ684-4−4i4i040-4−4i4i1-203-3-120−3i3i−i2ii−2i1-203-300-120−i2ii−2i−3i3i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ694-4−4i4i040-4−4i4i1-20-33-1203i−3i−i2ii−2i1-20-3300-120−i2ii−2i3i−3i0000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000
χ704-4−4i4i040-4−4i4i1-20-33-1203i−3i−i2ii−2i1-20-3300-120−i2ii−2i3i−3i00000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000
χ714-4−4i4i0-2022i−2i44000-4-4000−4i−4i4i4i-2-2000002202i2i−2i−2i00004-4−4i4i00-22000000002i−2i000000000000000000000000000000
χ724-4−4i4i0-2022i−2i44000-4-4000−4i−4i4i4i-2-2000002202i2i−2i−2i0000-444i−4i002-200000000−2i2i000000000000000000000000000000
χ7388888-48-4-4-42-4-4222-4-4222-42-4-12-4-1-122-12-4-12-12-1-122000000000000000000000000000000000000000000000000
χ7488888-48-4-4-4-42-4-4-4-42-4-4-4-42-422-1222-1-12-122-12-122-1-1000000000000000000000000000000000000000000000000
χ758888-8-4-8-4-4-42-44-2-22-44-2-22-42-4-12411-2-2-124-12-1211-2-2000000000000000000000000000000000000000000000000
χ768888-8-4-8-4-4-4-42444-42444-42-422-1-2-2-2112-1-22-12-1-2-211000000000000000000000000000000000000000000000000
χ7788-8-88-4-8-4442-4-4222-44-2-2-24-24-12-4-1-122-1241-21-211-2-2000000000000000000000000000000000000000000000000
χ7888-8-88-4-8-444-42-4-4-4-424444-24-22-1222-1-12-1-2-21-21-2-211000000000000000000000000000000000000000000000000
χ7988-8-8-8-48-4442-44-2-22-4-422-24-24-12411-2-2-12-41-21-2-1-122000000000000000000000000000000000000000000000000
χ8088-8-8-8-48-444-42444-42-4-4-44-24-22-1-2-2-2112-12-21-2122-1-1000000000000000000000000000000000000000000000000
χ818-88i−8i080-88i−8i-420004-2000−4i2i4i−2i-42000004-20−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ828-88i−8i0-404−4i4i2-406-6-2406i−6i2i−4i−2i4i-120-33001-20−i2ii−2i−3i3i00000000000000000000000000000000000000000000000000
χ838-88i−8i0-404−4i4i2-40-66-240−6i6i2i−4i−2i4i-1203-3001-20−i2ii−2i3i−3i00000000000000000000000000000000000000000000000000
χ848-88i−8i0-404−4i4i-420004-2000−4i2i4i−2i2-1000−3i33i3-2102i−i−2ii0033−33000000000000000000000000000000000000000000000000
χ858-88i−8i0-404−4i4i-420004-2000−4i2i4i−2i2-10003i3−3i3-2102i−i−2ii00−3333000000000000000000000000000000000000000000000000
χ868-8−8i8i080-8−8i8i-420004-20004i−2i−4i2i-42000004-204i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ878-8−8i8i0-4044i−4i2-406-6-240−6i6i−2i4i2i−4i-120-33001-20i−2i−i2i3i−3i00000000000000000000000000000000000000000000000000
χ888-8−8i8i0-4044i−4i2-40-66-2406i−6i−2i4i2i−4i-1203-3001-20i−2i−i2i−3i3i00000000000000000000000000000000000000000000000000
χ898-8−8i8i0-4044i−4i-420004-20004i−2i−4i2i2-1000−3i33i3-210−2ii2i−i00−3333000000000000000000000000000000000000000000000000
χ908-8−8i8i0-4044i−4i-420004-20004i−2i−4i2i2-10003i3−3i3-210−2ii2i−i0033−33000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.