Finite Group Databasebeta

← Group #13140240

Character table — Group #13140240

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222224444444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-111-1-1111-1-11-1-11-111-1-11111-1-1-11-1-1-1-1111-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1011-1-111-1-1111-1-11-1-11-111-1-11111-1-1-11-1-1-1-1111-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1111-1-111-1-1111-1-11-1-11-111-1-11111-1-1-11-1-1-1-1111-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ1211-1-111-1-1111-1-11-1-11-111-1-11111-1-1-11-1-1-1-1111-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ1311-1-111-1-1111-1-11-1-1-11-1-1111111-1-1-11-1-1-1-1111-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−ii11-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ1411-1-111-1-1111-1-11-1-1-11-1-1111111-1-1-11-1-1-1-1111-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i11-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1511-1-111-1-1111-1-11-1-1-11-1-1111111-1-1-11-1-1-1-1111-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611-1-111-1-1111-1-11-1-1-11-1-1111111-1-1-11-1-1-1-1111-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1222200000000220000-1-1-1-100000000-1-1-1-100000000
χ1822222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-20000111100000000111100000000
χ192222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-211-2-21111111111222200000000-2-20000-1-1-1-100000000111100000000
χ222222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-211-2-21111111111-2-2-2-200000000220000111100000000-1-1-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-111-2-211-2-2111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-111-2-211-2-21111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ252222-2-2-2-222-222-2-2-2000000222-222-2222-2-2-2-2-2-222-222-2-2-200000000000000002-22-2000000000000002-22-200000000000000000000
χ262222-2-2-2-222-222-2-2-2000000222-222-2222-2-2-2-2-2-222-222-2-2-20000000000000000-22-2200000000000000-22-2200000000000000000000
χ272222-2-2-2-222-222-2-2-20000002-12-222-2-1-1-111-211-2-1-11-1-1111003−3003−333−3−333−3−32-22-200000000000000-11-11000000003−33−300000000
χ282222-2-2-2-222-222-2-2-20000002-12-222-2-1-1-111-211-2-1-11-1-1111003−3003−333−3−333−3−3-22-22000000000000001-11-100000000−33−3300000000
χ292222-2-2-2-222-222-2-2-20000002-12-222-2-1-1-111-211-2-1-11-1-111100−3300−33−3−333−3−3332-22-200000000000000-11-1100000000−33−3300000000
χ302222-2-2-2-222-222-2-2-20000002-12-222-2-1-1-111-211-2-1-11-1-111100−3300−33−3−333−3−333-22-22000000000000001-11-1000000003−33−300000000
χ3122-2-222-2-2222-2-22-2-22-222-2-22-122-2-2-2-111112-1-1-2-1-1-11111-122-1-1-2-211-1-1-1-1111122-2-2000000002-20000-1-11100000000-1-11100000000
χ3222-2-222-2-2222-2-22-2-22-222-2-22-122-2-2-2-111112-1-1-2-1-1-11111-122-1-1-2-211-1-1-1-11111-2-22200000000-22000011-1-10000000011-1-100000000
χ3322-2-222-2-2222-2-22-2-22-222-2-2-12-1-11112-2-2-2-2-1221-1-1-11111-1-1-12211-2-2-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ3422-2-222-2-2222-2-22-2-22-222-2-2-12-1-11112-2-2-2-2-1221-1-1-11111-1-1-12211-2-2-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ3522-2-222-2-2222-2-22-2-2-22-2-2222-122-2-2-2-111112-1-1-2-1-1-11111-1-2-21122-1-11111-1-1-1-122-2-200000000-220000-1-1110000000011-1-100000000
χ3622-2-222-2-2222-2-22-2-2-22-2-2222-122-2-2-2-111112-1-1-2-1-1-11111-1-2-21122-1-11111-1-1-1-1-2-222000000002-2000011-1-100000000-1-11100000000
χ3722-2-222-2-2222-2-22-2-2-22-2-222-12-1-11112-2-2-2-2-1221-1-1-11111-111-2-2-1-1221111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ3822-2-222-2-2222-2-22-2-2-22-2-222-12-1-11112-2-2-2-2-1221-1-1-11111-111-2-2-1-1221111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ3922-2-2-2-22222-2-2-2-222000000222-2-2-222-2-222-2-2-2222-2-2-222-200000000000000002-2-22000000000000002-2-2200000000000000000000
χ4022-2-2-2-22222-2-2-2-222000000222-2-2-222-2-222-2-2-2222-2-2-222-20000000000000000-222-200000000000000-222-200000000000000000000
χ4122-2-2-2-22222-2-2-2-2220000002-12-2-2-22-111-1-1-2112-1-1111-1-11003−300−3333−3−3−3−3332-2-2200000000000000-111-1000000003−3−3300000000
χ4222-2-2-2-22222-2-2-2-2220000002-12-2-2-22-111-1-1-2112-1-1111-1-11003−300−3333−3−3−3−333-222-2000000000000001-1-1100000000−333−300000000
χ4322-2-2-2-22222-2-2-2-2220000002-12-2-2-22-111-1-1-2112-1-1111-1-1100−33003−3−3−33333−3−32-2-2200000000000000-111-100000000−333−300000000
χ4422-2-2-2-22222-2-2-2-2220000002-12-2-2-22-111-1-1-2112-1-1111-1-1100−33003−3−3−33333−3−3-222-2000000000000001-1-11000000003−3−3300000000
χ452-22-22-22-22-2-22-222-200000022-2-22-22-22-22-222-2-22-2-22-22-220000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ462-22-22-22-22-2-22-222-200000022-2-22-22-22-22-222-2-22-2-22-22-22000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ472-22-22-22-22-2-22-222-2000000-1211-11-1-22-22-2-12-21-111-11-11-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i3000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−3
χ482-22-22-22-22-2-22-222-2000000-1211-11-1-22-22-2-12-21-111-11-11-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−33
χ492-22-22-22-22-2-22-222-2000000-1211-11-1-22-22-2-12-21-111-11-11-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−33
χ502-22-22-22-22-2-22-222-2000000-1211-11-1-22-22-2-12-21-111-11-11-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
χ512-22-2-22-222-222-2-2-2200000022-222-2-2-22-2-22-2-2222-222-2-22-2000000000000000000002-22-2000000000000002-22-20000000000000000
χ522-22-2-22-222-222-2-2-2200000022-222-2-2-22-2-22-2-2222-222-2-22-200000000000000000000-22-2200000000000000-22-220000000000000000
χ532-2-222-2-222-2-2-222-2200000022-2-2-22-2-2-22-2222-222-2-2-22-2220000000000000000000000002-2-2200000000000000000000002-2-220000
χ542-2-222-2-222-2-2-222-2200000022-2-2-22-2-2-22-2222-222-2-2-22-222000000000000000000000000-222-20000000000000000000000-222-20000
χ552-2-222-2-222-2-2-222-22000000-12111-11-2-22-22-12-2-1-1111-11-1-1−i3i300i3−i300−i3i3−i3i3i3−i3i3−i3000000002-2-220000000000000000000000-111-1−i3i3i3−i3
χ562-2-222-2-222-2-2-222-22000000-12111-11-2-22-22-12-2-1-1111-11-1-1−i3i300i3−i300−i3i3−i3i3i3−i3i3−i300000000-222-200000000000000000000001-1-11i3−i3−i3i3
χ572-2-222-2-222-2-2-222-22000000-12111-11-2-22-22-12-2-1-1111-11-1-1i3−i300−i3i300i3−i3i3−i3−i3i3−i3i3000000002-2-220000000000000000000000-111-1i3−i3−i3i3
χ582-2-222-2-222-2-2-222-22000000-12111-11-2-22-22-12-2-1-1111-11-1-1i3−i300−i3i300i3−i3i3−i3−i3i3−i3i300000000-222-200000000000000000000001-1-11−i3i3i3−i3
χ592-2-22-222-22-22-22-22-200000022-22-222-2-222-2-2-22-22-22-222-2-2000000000000000000002i−2i−2i2i000000000000002i−2i−2i2i0000000000000000
χ602-2-22-222-22-22-22-22-200000022-22-222-2-222-2-2-22-22-22-222-2-200000000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i0000000000000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ634444-4-4-4-444-444-4-4-4000000-24-22-2-22444-4-42-4-42-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-444-444-4-4-4000000-2-2-22-2-22-2-2-222222211-111-1-1-10023−230023−23−3−333−3−333000000000000000000000000000000000000000000
χ654444-4-4-4-444-444-4-4-4000000-2-2-22-2-22-2-2-222222211-111-1-1-100−232300−232333−3−333−3−3000000000000000000000000000000000000000000
χ6644-4-444-4-4444-4-44-4-44-444-4-4-2-2-2-2222-22222-2-2-22111-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000000000000000
χ6744-4-444-4-4444-4-44-4-4-44-4-444-2-2-2-2222-22222-2-2-22111-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6844-4-4-4-44444-4-4-4-444000000-24-2222-24-4-4442-4-4-2-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ6944-4-4-4-44444-4-4-4-444000000-2-2-2222-2-222-2-2222-211-1-1-111-10023−2300−2323−3−33333−3−3000000000000000000000000000000000000000000
χ7044-4-4-4-44444-4-4-4-444000000-2-2-2222-2-222-2-2222-211-1-1-111-100−23230023−2333−3−3−3−333000000000000000000000000000000000000000000
χ714-44-44-44-44-4-44-444-40000004-2-4-44-442-22-224-22-4-222-22-22-20000000000000000000000000000000000000000000000000000000000
χ724-44-44-44-44-4-44-444-4000000-2-222-22-22-22-22-2-2221-1-11-11-11−2i32i300−2i32i300i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000000000
χ734-44-44-44-44-4-44-444-4000000-2-222-22-22-22-22-2-2221-1-11-11-112i3−2i3002i3−2i300−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
χ744-44-4-44-444-444-4-4-440000004-2-444-4-42-222-2-42-24-22-2-222-220000000000000000000000000000000000000000000000000000000000
χ754-44-4-44-444-444-4-4-44000000-242-2-222-44-4-442-44-2-22-2-222-220000000000000000000000000000000000000000000000000000000000
χ764-44-4-44-444-444-4-4-44000000-2-22-2-2222-222-222-2-21-111-1-11-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ774-44-4-44-444-444-4-4-44000000-2-22-2-2222-222-222-2-21-111-1-11-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ784-4-444-4-444-4-4-444-440000004-2-4-4-44-422-22-24-224-2222-22-2-20000000000000000000000000000000000000000000000000000000000
χ794-4-444-4-444-4-4-444-44000000-2-2222-2222-22-2-2-22-21-1-1-11-111−2i32i3002i3−2i300i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000000000
χ804-4-444-4-444-4-4-444-44000000-2-2222-2222-22-2-2-22-21-1-1-11-1112i3−2i300−2i32i300−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
χ814-4-44-444-44-44-44-44-40000004-2-44-44422-2-22-42-2-4-22-22-2-2220000000000000000000000000000000000000000000000000000000000
χ824-4-44-444-44-44-44-44-4000000-242-22-2-2-4-444-42-442-22-22-2-2220000000000000000000000000000000000000000000000000000000000
χ834-4-44-444-44-44-44-44-4000000-2-22-22-2-222-2-2222-221-11-111-1-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ844-4-44-444-44-44-44-44-4000000-2-22-22-2-222-2-2222-221-11-111-1-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000222200000022000000-1-1-1-1-1-1-1-1000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-2-2-2000000-2-200000011111111000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002222000000-2-2000000-1-1-1-11111000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-2-2-2000000220000001111-1-1-1-1000000000000
χ8966-6-666-6-6-3-3-333-3336-6-3-333000000000000000000000000000000000000000000002i2i−2i−2i0000002i−2i000000−i−iii−i−iii000000000000
χ9066-6-666-6-6-3-3-333-3336-6-3-33300000000000000000000000000000000000000000000−2i−2i2i2i000000−2i2i000000ii−i−iii−i−i000000000000
χ9166-6-666-6-6-3-3-333-333-6633-3-3000000000000000000000000000000000000000000002i2i−2i−2i000000−2i2i000000−i−iiiii−i−i000000000000
χ9266-6-666-6-6-3-3-333-333-6633-3-300000000000000000000000000000000000000000000−2i−2i2i2i0000002i−2i000000ii−i−i−i−iii000000000000
χ936-66-6-66-66-33-3-3333-30033−3333−33000000000000000000000000000000000000000000002-22-200000000000000-11-113−33−3000000000000
χ946-66-6-66-66-33-3-3333-30033−3333−3300000000000000000000000000000000000000000000-22-22000000000000001-11-1−33−33000000000000
χ956-66-6-66-66-33-3-3333-300−3333−3333000000000000000000000000000000000000000000002-22-200000000000000-11-11−33−33000000000000
χ966-66-6-66-66-33-3-3333-300−3333−333300000000000000000000000000000000000000000000-22-22000000000000001-11-13−33−3000000000000
χ976-6-66-666-6-33-33-33-330033−33−3333000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−ii3−i3−i3i3000000000000
χ986-6-66-666-6-33-33-33-330033−33−333300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−i3i3i3−i3000000000000
χ996-6-66-666-6-33-33-33-3300−333333−33000000000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−i3i3i3−i3000000000000
χ1006-6-66-666-6-33-33-33-3300−333333−3300000000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−iii3−i3−i3i3000000000000
χ10112121212-12-12-12-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-12-12-121212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-1212-1212-1212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-121212-12-1212-6666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).