Finite Group Databasebeta

← Group #11721154

Character table — Group #11721154

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222446666666666669999121212121212121212121818181818181818181818181818181818183636363636363636
order12223446661212336666661212121244443666121212121212222244444466661212121266121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ611111-1-1111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ711111-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1
χ811111-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-111
χ911-1-11i−i1-1-1i−i11-11-11-1-1ii−i−iii−i−i11-1-1i−iii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i1-1i−i1-1i−i
χ1011-1-11i−i1-1-1i−i11-11-11-1-1ii−i−iii−i−i11-1-1i−iii−i−i1-1-11−ii-11−ii11-1-1ii−i−i-11−ii-11−ii
χ1111-1-11i−i1-1-1i−i11-11-11-1-1ii−i−i−i−iii11-1-1i−iii−i−i-111-1i−i-11−ii-1-111−i−iii1-1i−i-11−ii
χ1211-1-11i−i1-1-1i−i11-11-11-1-1ii−i−i−i−iii11-1-1i−iii−i−i-11-11−ii1-1i−i-1-111−i−iii-11−ii1-1i−i
χ1311-1-11−ii1-1-1−ii11-11-11-1-1−i−iiiii−i−i11-1-1−ii−i−iii-111-1−ii-11i−i-1-111ii−i−i1-1−ii-11i−i
χ1411-1-11−ii1-1-1−ii11-11-11-1-1−i−iiiii−i−i11-1-1−ii−i−iii-11-11i−i1-1−ii-1-111ii−i−i-11i−i1-1−ii
χ1511-1-11−ii1-1-1−ii11-11-11-1-1−i−iii−i−iii11-1-1−ii−i−iii1-11-1−ii1-1−ii11-1-1−i−iii1-1−ii1-1−ii
χ1611-1-11−ii1-1-1−ii11-11-11-1-1−i−iii−i−iii11-1-1−ii−i−iii1-1-11i−i-11i−i11-1-1−i−iii-11i−i-11i−i
χ172222222222222-12-1-122-1-1-1-1-12222-1-1-1-122-1-1-1-12200000000-1-1-1-1-1-1-1-100000000
χ182222222222222-12-1-122-1-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-2-2000000001111111100000000
χ19222222222222-12-122-1-1222220000-1-1-1-1-1-1-1-1-1-10000002222000000000000-1-1-1-1
χ20222222222222-12-122-1-1222220000-1-1-1-1-1-1-1-1-1-1000000-2-2-2-20000000000001111
χ2122222-2-2222-2-22-12-1-122-111112222-1-1-1-1-2-21111-2-2000000001111-1-1-1-100000000
χ2222222-2-2222-2-22-12-1-122-11111-2-2-2-2-1-1-1-1-2-211112200000000-1-1-1-1111100000000
χ2322222-2-2222-2-2-12-122-1-12-2-2-2-20000-1-1-1-111111100000022-2-2000000000000-1-111
χ2422222-2-2222-2-2-12-122-1-12-2-2-2-20000-1-1-1-1111111000000-2-22200000000000011-1-1
χ2522-2-222i−2i2-2-22i−2i2-1-2-112-21−i−iii2i2i−2i−2i-1-1112i−2i−i−iii2-200000000-1-111−i−iii00000000
χ2622-2-222i−2i2-2-22i−2i2-1-2-112-21−i−iii−2i−2i2i2i-1-1112i−2i−i−iii-220000000011-1-1ii−i−i00000000
χ2722-2-222i−2i2-2-22i−2i-1212-2-11-22i2i−2i−2i0000-1-111−ii−i−iii0000002-22i−2i000000000000-11−ii
χ2822-2-222i−2i2-2-22i−2i-1212-2-11-22i2i−2i−2i0000-1-111−ii−i−iii000000-22−2i2i0000000000001-1i−i
χ2922-2-22−2i2i2-2-2−2i2i2-1-2-112-21ii−i−i2i2i−2i−2i-1-111−2i2iii−i−i-220000000011-1-1−i−iii00000000
χ3022-2-22−2i2i2-2-2−2i2i2-1-2-112-21ii−i−i−2i−2i2i2i-1-111−2i2iii−i−i2-200000000-1-111ii−i−i00000000
χ3122-2-22−2i2i2-2-2−2i2i-1212-2-11-2−2i−2i2i2i0000-1-111i−iii−i−i0000002-2−2i2i000000000000-11i−i
χ3222-2-22−2i2i2-2-2−2i2i-1212-2-11-2−2i−2i2i2i0000-1-111i−iii−i−i000000-222i−2i0000000000001-1−ii
χ332-22-2200-2-2200222-22-2-2-200002i−2i2i−2i2-22-2000000000000000000002i−2i2i−2i00000000
χ342-22-2200-2-2200222-22-2-2-20000−2i2i−2i2i2-22-200000000000000000000−2i2i−2i2i00000000
χ352-22-2200-2-22002-121-1-2-213−33−32i−2i2i−2i-11-11003−33−30000000000−i3i3−i3i3−ii−ii00000000
χ362-22-2200-2-22002-121-1-2-213−33−3−2i2i−2i2i-11-11003−33−30000000000i3−i3i3−i3i−ii−i00000000
χ372-22-2200-2-22002-121-1-2-21−33−332i−2i2i−2i-11-1100−33−330000000000i3−i3i3−i3−ii−ii00000000
χ382-22-2200-2-22002-121-1-2-21−33−33−2i2i−2i2i-11-1100−33−330000000000−i3i3−i3i3i−ii−i00000000
χ392-2-22200-22-20022-2-2-2-22200002-2-222-2-22000000000000000000002-2-2200000000
χ402-2-22200-22-20022-2-2-2-2220000-222-22-2-2200000000000000000000-222-200000000
χ412-2-22200-22-2002-1-211-22-1−i3i3i3−i32-2-22-111-100−i3i3i3−i30000000000−i3i3i3−i3-111-100000000
χ422-2-22200-22-2002-1-211-22-1−i3i3i3−i3-222-2-111-100−i3i3i3−i30000000000i3−i3−i3i31-1-1100000000
χ432-2-22200-22-2002-1-211-22-1i3−i3−i3i32-2-22-111-100i3−i3−i3i30000000000i3−i3−i3i3-111-100000000
χ442-2-22200-22-2002-1-211-22-1i3−i3−i3i3-222-2-111-100i3−i3−i3i30000000000−i3i3i3−i31-1-1100000000
χ45444444444444-2-2-2-2-2-2-2-2-2-2-2-200001111-2-2111100000000000000000000000000
χ4644444-4-4444-4-4-2-2-2-2-2-2-2-222220000111122-1-1-1-100000000000000000000000000
χ4744-4-444i−4i4-4-44i−4i-2-22-22-222−2i−2i2i2i000011-1-1−2i2iii−i−i00000000000000000000000000
χ4844-4-44−4i4i4-4-4−4i4i-2-22-22-2222i2i−2i−2i000011-1-12i−2i−i−iii00000000000000000000000000
χ494-44-4400-4-4400-24-2-4422-400000000-22-2200000000000000000000000000000000
χ504-44-4400-4-4400-2-2-22-222223−2323−2300001-11-100−33−3300000000000000000000000000
χ514-44-4400-4-4400-2-2-22-2222−2323−232300001-11-1003−33−300000000000000000000000000
χ524-4-44400-44-400-242-4-42-2400000000-222-200000000000000000000000000000000
χ534-4-44400-44-400-2-22222-2-2−2i32i32i3−2i300001-1-1100i3−i3−i3i300000000000000000000000000
χ544-4-44400-44-400-2-22222-2-22i3−2i3−2i32i300001-1-1100−i3i3i3−i300000000000000000000000000
χ556666-366-3-3-3-3-300000000000000000000000000002222000000000000-1-1-1-10000
χ566666-366-3-3-3-3-30000000000000000000000000000-2-2-2-200000000000011110000
χ576666-3-6-6-3-3-333000000000000000000000000000022-2-2000000000000-1-1110000
χ586666-3-6-6-3-3-3330000000000000000000000000000-2-22200000000000011-1-10000
χ5966-6-6-36i−6i-333−3i3i00000000000000000000000000002-22i−2i000000000000-11−ii0000
χ6066-6-6-36i−6i-333−3i3i0000000000000000000000000000-22−2i2i0000000000001-1i−i0000
χ6166-6-6-3−6i6i-3333i−3i00000000000000000000000000002-2−2i2i000000000000-11i−i0000
χ6266-6-6-3−6i6i-3333i−3i0000000000000000000000000000-222i−2i0000000000001-1−ii0000
χ6312-1212-12-60066-6000000000000000000000000000000000000000000000000000000
χ6412-12-1212-6006-66000000000000000000000000000000000000000000000000000000

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