Finite Group Databasebeta

← Group #72268344

Character table — Group #72268344

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122668888121616161616161616242424243232323232323232323232324848111122668888121616161616161616242424243232323232323232323232324848
order12222222224423366666644446666666612121212442222222222442666666664444666666661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211
χ31111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211
χ411111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1
χ511111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32-1-111111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32-1-1
χ611111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32-1-111111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32-1-1
χ71111-1-11111-1-1-1111111111-11-1-1-111-1-111-1-1-1-11-11111-1-11111-1-1-1111111111-11-1-1-111-1-111-1-1-1-11-1
χ81111-1-11111-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i321-11111-1-11111-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i321-1
χ91111-1-11111-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i321-11111-1-11111-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i321-1
χ101111-1-111-1-111-1111111111-11-1-1-1-1-1-1-1-1-11111-111111-1-111-1-111-1111111111-11-1-1-1-1-1-1-1-1-11111-11
χ111111-1-111-1-111-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111111-1-111-1-111-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11
χ121111-1-111-1-111-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111111-1-111-1-111-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11
χ13333333333333300000000-1-1-1-1000000000000-1-1333333333333300000000-1-1-1-1000000000000-1-1
χ1433333333-3-3-3-3300000000-1-1-1-10000000000001133333333-3-3-3-3300000000-1-1-1-100000000000011
χ153333-3-33333-3-3-300000000-11-11000000000000-113333-3-33333-3-3-300000000-11-11000000000000-11
χ163333-3-333-3-333-300000000-11-110000000000001-13333-3-333-3-333-300000000-11-110000000000001-1
χ1744-4-4004-400000-2-22-22-22200000000000000000044-4-4004-400000-2-22-22-222000000000000000000
χ1844-4-4004-4000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i300000000000000000044-4-4004-4000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000000000
χ1944-4-4004-4000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i300000000000000000044-4-4004-4000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000000000
χ204-4-444-4002-22-2011-1-1-1-11100001-11-11-11-11-11-1004-4-444-4002-22-2011-1-1-1-11100001-11-11-11-11-11-100
χ214-4-444-4002-22-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1−i321+i32004-4-444-4002-22-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1−i321+i3200
χ224-4-444-4002-22-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1+i321−i32004-4-444-4002-22-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1+i321−i3200
χ234-4-444-400-22-22011-1-1-1-11100001-1-111-1-11-11-11004-4-444-400-22-22011-1-1-1-11100001-1-111-1-11-11-1100
χ244-4-444-400-22-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i32004-4-444-400-22-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i3200
χ254-4-444-400-22-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i32004-4-444-400-22-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i3200
χ264-4-44-44002-2-22011-1-1-1-1110000-111-1-111-1-11-11004-4-44-44002-2-22011-1-1-1-1110000-111-1-111-1-11-1100
χ274-4-44-44002-2-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321+i32−1−i32004-4-44-44002-2-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321+i32−1−i3200
χ284-4-44-44002-2-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321−i32−1+i32004-4-44-44002-2-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321−i32−1+i3200
χ294-4-44-4400-222-2011-1-1-1-1110000-11-11-11-111-11-1004-4-44-4400-222-2011-1-1-1-1110000-11-11-11-111-11-100
χ304-4-44-4400-222-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i32004-4-44-4400-222-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i3200
χ314-4-44-4400-222-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i32004-4-44-4400-222-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i3200
χ32666666-2-20000-20000000022-2-200000000000000666666-2-20000-20000000022-2-200000000000000
χ33666666-2-20000-200000000-2-22200000000000000666666-2-20000-200000000-2-22200000000000000
χ346666-6-6-2-200002000000002-2-22000000000000006666-6-6-2-200002000000002-2-2200000000000000
χ356666-6-6-2-20000200000000-222-2000000000000006666-6-6-2-20000200000000-222-200000000000000
χ368-88-8000000000222-22-2-2-20000000000000000008-88-8000000000222-22-2-2-2000000000000000000
χ378-88-8000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000000000008-88-8000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i3000000000000000000
χ388-88-8000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000000000008-88-8000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i3000000000000000000
χ391212-12-1200-4400000000000000000000000000000001212-12-1200-440000000000000000000000000000000
χ40111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321+i321+i321−i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32-1-1
χ421111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321+i321−i321−i321+i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32-1-1
χ4311111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ4411111111-1-1-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32-1-1-1-1-1-1-1-1-1-11111-11−i321+i321−i321−i321+i321+i321−i321+i32-1-1-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211
χ4511111111-1-1-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32-1-1-1-1-1-1-1-1-1-11111-11+i321−i321+i321+i321−i321−i321+i321−i32-1-1-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211
χ461111-1-11111-1-1-1111111111-11-1-1-111-1-111-1-1-1-11-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-11-1111-1-111-1-11111-11
χ471111-1-11111-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i321-1-1-1-1-111-1-1-1-11111−i321+i321−i321−i321+i321+i321−i321+i32-11-11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11
χ481111-1-11111-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i321-1-1-1-1-111-1-1-1-11111+i321−i321+i321+i321−i321−i321+i321−i32-11-11−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11
χ491111-1-111-1-111-1111111111-11-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-111-1-11-1-1-1-1-1-1-1-1-11-1111111111-1-1-1-11-1
χ501111-1-111-1-111-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11-1-1-1-111-1-111-1-111−i321+i321−i321−i321+i321+i321−i321+i32-11-11−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321-1
χ511111-1-111-1-111-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11-1-1-1-111-1-111-1-111+i321−i321+i321+i321−i321−i321+i321−i32-11-11−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321-1
χ52333333333333300000000-1-1-1-1000000000000-1-1-3-3-3-3-3-3-3-3-3-3-3-3-300000000111100000000000011
χ5333333333-3-3-3-3300000000-1-1-1-100000000000011-3-3-3-3-3-3-3-33333-3000000001111000000000000-1-1
χ543333-3-33333-3-3-300000000-11-11000000000000-11-3-3-3-333-3-3-3-3333000000001-11-10000000000001-1
χ553333-3-333-3-333-300000000-11-110000000000001-1-3-3-3-333-3-333-3-33000000001-11-1000000000000-11
χ5644-4-4004-400000-2-22-22-222000000000000000000-4-44400-440000022-22-22-2-2000000000000000000
χ5744-4-4004-4000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000000000-4-44400-4400000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i3000000000000000000
χ5844-4-4004-4000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000000000-4-44400-4400000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i3000000000000000000
χ594-4-444-4002-22-2011-1-1-1-11100001-11-11-11-11-11-100-444-4-4400-22-220-1-11111-1-10000-11-11-11-11-11-1100
χ604-4-444-4002-22-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1−i321+i3200-444-4-4400-22-2201−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i3200001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321+i32−1−i3200
χ614-4-444-4002-22-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1+i321−i3200-444-4-4400-22-2201+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i3200001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321−i32−1+i3200
χ624-4-444-400-22-22011-1-1-1-11100001-1-111-1-11-11-1100-444-4-44002-22-20-1-11111-1-10000-111-1-111-11-11-100
χ634-4-444-400-22-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i320000−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321−i32−1+i321+i32−1−i3200-444-4-44002-22-201−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i3200001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i32−1+i321−i32−1−i321+i3200
χ644-4-444-400-22-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i320000−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321+i32−1−i321−i32−1+i3200-444-4-44002-22-201+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i3200001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−1−i321+i32−1+i321−i3200
χ654-4-44-44002-2-22011-1-1-1-1110000-111-1-111-1-11-1100-444-44-400-222-20-1-11111-1-100001-1-111-1-111-11-100
χ664-4-44-44002-2-220−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i321+i32−1−i3200-444-44-400-222-201−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i320000−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i32−1−i321+i3200
χ674-4-44-44002-2-220−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i321−i32−1+i3200-444-44-400-222-201+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i320000−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i32−1+i321−i3200
χ684-4-44-4400-222-2011-1-1-1-1110000-11-11-11-111-11-100-444-44-4002-2-220-1-11111-1-100001-11-11-11-1-11-1100
χ694-4-44-4400-222-20−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3200001−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−1+i321−i32−1−i321+i3200-444-44-4002-2-2201−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i320000−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321−i32−1+i321+i32−1−i3200
χ704-4-44-4400-222-20−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3200001+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−1−i321+i32−1+i321−i3200-444-44-4002-2-2201+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i320000−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321+i32−1−i321−i32−1+i3200
χ71666666-2-20000-20000000022-2-200000000000000-6-6-6-6-6-6220000200000000-2-22200000000000000
χ72666666-2-20000-200000000-2-22200000000000000-6-6-6-6-6-622000020000000022-2-200000000000000
χ736666-6-6-2-200002000000002-2-2200000000000000-6-6-6-666220000-200000000-222-200000000000000
χ746666-6-6-2-20000200000000-222-200000000000000-6-6-6-666220000-2000000002-2-2200000000000000
χ758-88-8000000000222-22-2-2-2000000000000000000-88-88000000000-2-2-22-2222000000000000000000
χ768-88-8000000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i3000000000000000000-88-880000000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000000000
χ778-88-8000000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i3000000000000000000-88-880000000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000000000
χ781212-12-1200-440000000000000000000000000000000-12-121212004-40000000000000000000000000000000

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