Finite Group Databasebeta

← Group #11721123

Character table — Group #11721123

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222446666666666669999121212121212121212121818181818181818181818181818181818183636363636363636
order1222344666121233666666121212124444366612121212121222224444441212121212121212666612121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111-1-1111-1-111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111
χ611111-1-1111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1
χ711111-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ811111-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ91-11-11i−i1-1-1i−i111-1-11-1-1ii−i−iii−i−i11-1-1i−iii−i−i1-11-11-1i−ii−iii−i−i11-1-11-11-1i−ii−i
χ101-11-11i−i1-1-1i−i111-1-11-1-1ii−i−iii−i−i11-1-1i−iii−i−i-11-111-1−ii−iiii−i−i11-1-1-11-11−ii−ii
χ111-11-11i−i1-1-1i−i111-1-11-1-1ii−i−i−i−iii11-1-1i−iii−i−i1-1-11-11i−i−ii−i−iii-1-1111-1-11i−i−ii
χ121-11-11i−i1-1-1i−i111-1-11-1-1ii−i−i−i−iii11-1-1i−iii−i−i-111-1-11−iii−i−i−iii-1-111-111-1−iii−i
χ131-11-11−ii1-1-1−ii111-1-11-1-1−i−iiiii−i−i11-1-1−ii−i−iii1-1-11-11−iii−iii−i−i-1-1111-1-11−iii−i
χ141-11-11−ii1-1-1−ii111-1-11-1-1−i−iiiii−i−i11-1-1−ii−i−iii-111-1-11i−i−iiii−i−i-1-111-111-1i−i−ii
χ151-11-11−ii1-1-1−ii111-1-11-1-1−i−iii−i−iii11-1-1−ii−i−iii1-11-11-1−ii−ii−i−iii11-1-11-11-1−ii−ii
χ161-11-11−ii1-1-1−ii111-1-11-1-1−i−iii−i−iii11-1-1−ii−i−iii-11-111-1i−ii−i−i−iii11-1-1-11-11i−ii−i
χ172222222222222-1-12-122-122220000-1-1-1-1-1-1-1-1-1-100220000220000000000-1-100-1-1
χ182222222222222-1-12-122-122220000-1-1-1-1-1-1-1-1-1-100-2-20000-2-20000000000110011
χ19222222222222-122-12-1-12-1-1-1-12222-1-1-1-122-1-1-1-10000220000-1-1-1-1-1-1-1-100000000
χ20222222222222-122-12-1-12-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-10000-2-200001111111100000000
χ2122222-2-2222-2-22-1-12-122-1-2-2-2-20000-1-1-1-111111100220000-2-20000000000-1-10011
χ2222222-2-2222-2-22-1-12-122-1-2-2-2-20000-1-1-1-111111100-2-200002200000000001100-1-1
χ2322222-2-2222-2-2-122-12-1-1211112222-1-1-1-1-2-211110000-2-20000-1-1-1-1111100000000
χ2422222-2-2222-2-2-122-12-1-121111-2-2-2-2-1-1-1-1-2-2111100002200001111-1-1-1-100000000
χ2522-2-2200-22-20022-222-2-2-200002i−2i2i−2i2-2-2200000000000000002i−2i2i−2i000000000000
χ2622-2-2200-22-20022-222-2-2-20000−2i2i−2i2i2-2-220000000000000000−2i2i−2i2i000000000000
χ2722-2-2200-22-200-12-2-1211-2−i3i3−i3i32i−2i2i−2i-111-100−i3i3−i3i30000000000−ii−ii3−33−300000000
χ2822-2-2200-22-200-12-2-1211-2−i3i3−i3i3−2i2i−2i2i-111-100−i3i3−i3i30000000000i−ii−i−33−3300000000
χ2922-2-2200-22-200-12-2-1211-2i3−i3i3−i32i−2i2i−2i-111-100i3−i3i3−i30000000000−ii−ii−33−3300000000
χ3022-2-2200-22-200-12-2-1211-2i3−i3i3−i3−2i2i−2i2i-111-100i3−i3i3−i30000000000i−ii−i3−33−300000000
χ312-22-222i−2i2-2-22i−2i2-1-1-212-212i2i−2i−2i0000-1-111−ii−i−iii002-200002i−2i0000000000-1100−ii
χ322-22-222i−2i2-2-22i−2i2-1-1-212-212i2i−2i−2i0000-1-111−ii−i−iii00-220000−2i2i00000000001-100i−i
χ332-22-222i−2i2-2-22i−2i-1221-2-11-2−i−iii2i2i−2i−2i-1-1112i−2i−i−iii00002-20000−i−iii-1-11100000000
χ342-22-222i−2i2-2-22i−2i-1221-2-11-2−i−iii−2i−2i2i2i-1-1112i−2i−i−iii0000-220000ii−i−i11-1-100000000
χ352-22-22−2i2i2-2-2−2i2i2-1-1-212-21−2i−2i2i2i0000-1-111i−iii−i−i002-20000−2i2i0000000000-1100i−i
χ362-22-22−2i2i2-2-2−2i2i2-1-1-212-21−2i−2i2i2i0000-1-111i−iii−i−i00-2200002i−2i00000000001-100−ii
χ372-22-22−2i2i2-2-2−2i2i-1221-2-11-2ii−i−i2i2i−2i−2i-1-111−2i2iii−i−i0000-220000−i−iii11-1-100000000
χ382-22-22−2i2i2-2-2−2i2i-1221-2-11-2ii−i−i−2i−2i2i2i-1-111−2i2iii−i−i00002-20000ii−i−i-1-11100000000
χ392-2-22200-2-220022-2-2-2-22200002-2-222-22-200000000000000002-2-22000000000000
χ402-2-22200-2-220022-2-2-2-2220000-222-22-22-20000000000000000-222-2000000000000
χ412-2-22200-2-2200-12-21-21-123−3−332-2-22-11-11003−3−330000000000-111-1−333−300000000
χ422-2-22200-2-2200-12-21-21-123−3−33-222-2-11-11003−3−3300000000001-1-113−3−3300000000
χ432-2-22200-2-2200-12-21-21-12−333−32-2-22-11-1100−333−30000000000-111-13−3−3300000000
χ442-2-22200-2-2200-12-21-21-12−333−3-222-2-11-1100−333−300000000001-1-11−333−300000000
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
χ4744-4-4400-44-4004-224-2-4-4200000000-222-200000000000000000000000000000000
χ4844-4-4400-44-400-2-22-2-2222−2i32i3−2i32i300001-1-1100i3−i3i3−i300000000000000000000000000
χ4944-4-4400-44-400-2-22-2-22222i3−2i32i3−2i300001-1-1100−i3i3−i3i300000000000000000000000000
χ504-44-444i−4i4-4-44i−4i-2-2-222-222−2i−2i2i2i000011-1-1−2i2iii−i−i00000000000000000000000000
χ514-44-44−4i4i4-4-4−4i4i-2-2-222-2222i2i−2i−2i000011-1-12i−2i−i−iii00000000000000000000000000
χ524-4-44400-4-44004-22-42-44-200000000-22-2200000000000000000000000000000000
χ534-4-44400-4-4400-2-22222-2-223−23−232300001-11-100−333−300000000000000000000000000
χ544-4-44400-4-4400-2-22222-2-2−232323−2300001-11-1003−3−3300000000000000000000000000
χ556666-366-3-3-3-3-300000000000000000000000000220000220000000000-1-100-1-100
χ566666-366-3-3-3-3-300000000000000000000000000-2-20000-2-2000000000011001100
χ576666-3-6-6-3-3-33300000000000000000000000000220000-2-20000000000-1-1001100
χ586666-3-6-6-3-3-33300000000000000000000000000-2-200002200000000001100-1-100
χ596-66-6-36i−6i-333−3i3i000000000000000000000000002-200002i−2i0000000000-1100−ii00
χ606-66-6-36i−6i-333−3i3i00000000000000000000000000-220000−2i2i00000000001-100i−i00
χ616-66-6-3−6i6i-3333i−3i000000000000000000000000002-20000−2i2i0000000000-1100i−i00
χ626-66-6-3−6i6i-3333i−3i00000000000000000000000000-2200002i−2i00000000001-100−ii00
χ631212-12-12-6006-66000000000000000000000000000000000000000000000000000000
χ6412-12-1212-60066-6000000000000000000000000000000000000000000000000000000

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