Finite Group Databasebeta

← Group #11721314

Character table — Group #11721314

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222446666666666669999121212121212121212121818181818181818181818181818181818183636363636363636
order122222366666336666666666444436666666662244444444121212121212121266121212121212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111-1-11111-1-11111-1-1-1-1111111111-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ61111-1-11111-1-11111-1-1-1-1111111111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ81111-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111
χ911-1-11-111-1-11-1111-111-1-1-1-11-1ii−i−i11-11-1-111-1-11-11-1i−ii−ii−iii−i−iii−i−i1-1i−ii−i1-1
χ1011-1-11-111-1-11-1111-111-1-1-1-11-1ii−i−i11-11-1-111-1-1-11-11−iii−i−iiii−i−iii−i−i-11−ii−ii-11
χ1111-1-11-111-1-11-1111-111-1-1-1-11-1−i−iii11-11-1-111-1-11-11-1−ii−ii−ii−i−iii−i−iii1-1−ii−ii1-1
χ1211-1-11-111-1-11-1111-111-1-1-1-11-1−i−iii11-11-1-111-1-1-11-11i−i−iii−i−i−iii−i−iii-11i−ii−i-11
χ1311-1-1-1111-1-1-11111-1-1-111-1-11-1ii−i−i1-111-1-1-1-1111-1-11−ii−iii−iii−i−i−i−iii1-1i−i−ii-11
χ1411-1-1-1111-1-1-11111-1-1-111-1-11-1ii−i−i1-111-1-1-1-111-111-1i−i−ii−iiii−i−i−i−iii-11−iii−i1-1
χ1511-1-1-1111-1-1-11111-1-1-111-1-11-1−i−iii1-111-1-1-1-1111-1-11i−ii−i−ii−i−iiiii−i−i1-1−iii−i-11
χ1611-1-1-1111-1-1-11111-1-1-111-1-11-1−i−iii1-111-1-1-1-111-111-1−iii−ii−i−i−iiiii−i−i-11i−i−ii1-1
χ172222222222222-1222222-1-1-120000-1-1-1-1-1-1-1-1-1-1222200000000000000-1-10000-1-1
χ182222222222222-1222222-1-1-120000-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000011000011
χ19222222222222-12-1-1-1-1-1-1222-12222-122-1-1-1-1-1-1-10000002200-1-1-1-1-1-1-1-100000000
χ20222222222222-12-1-1-1-1-1-1222-1-2-2-2-2-122-1-1-1-1-1-1-1000000-2-2001111111100000000
χ212222-2-22222-2-22-122-2-2-2-2-1-1-120000-111-1-1-1111122-2-200000000000000-1-1000011
χ222222-2-22222-2-22-122-2-2-2-2-1-1-120000-111-1-1-11111-2-22200000000000000110000-1-1
χ232222-2-22222-2-2-12-1-11111222-12222-1-2-2-1-1-11111000000-2-200-1-1-1-1111100000000
χ242222-2-22222-2-2-12-1-11111222-1-2-2-2-2-1-2-2-1-1-1111100000022001111-1-1-1-100000000
χ2522-2-22-222-2-22-22-12-222-2-211-1-20000-1-11-111-1-1112-22-200000000000000-110000-11
χ2622-2-22-222-2-22-22-12-222-2-211-1-20000-1-11-111-1-111-22-22000000000000001-100001-1
χ2722-2-22-222-2-22-2-12-11-1-111-2-2212i2i−2i−2i-12-2-111-1-1110000002i−2i00−i−iii−i−iii00000000
χ2822-2-22-222-2-22-2-12-11-1-111-2-221−2i−2i2i2i-12-2-111-1-111000000−2i2i00ii−i−iii−i−i00000000
χ2922-2-2-2222-2-2-222-12-2-2-22211-1-20000-11-1-11111-1-12-2-2200000000000000-1100001-1
χ3022-2-2-2222-2-2-222-12-2-2-22211-1-20000-11-1-11111-1-1-222-2000000000000001-10000-11
χ3122-2-2-2222-2-2-22-12-1111-1-1-2-2212i2i−2i−2i-1-22-11111-1-1000000−2i2i00−i−iiiii−i−i00000000
χ3222-2-2-2222-2-2-22-12-1111-1-1-2-221−2i−2i2i2i-1-22-11111-1-10000002i−2i00ii−i−i−i−iii00000000
χ332-22-2002-22-20022-2200002-2-2-22i−2i2i−2i200-22-2000000000000002i−2i2i−2i000000000000
χ342-22-2002-22-20022-2200002-2-2-2−2i2i−2i2i200-22-200000000000000−2i2i−2i2i000000000000
χ352-22-2002-22-200-121-1−i3i3−i3i32-2-212i−2i2i−2i-1001-11−i3i3−i3i30000000000−ii−ii3−33−300000000
χ362-22-2002-22-200-121-1−i3i3−i3i32-2-21−2i2i−2i2i-1001-11−i3i3−i3i30000000000i−ii−i−33−3300000000
χ372-22-2002-22-200-121-1i3−i3i3−i32-2-212i−2i2i−2i-1001-11i3−i3i3−i30000000000−ii−ii−33−3300000000
χ382-22-2002-22-200-121-1i3−i3i3−i32-2-21−2i2i−2i2i-1001-11i3−i3i3−i30000000000i−ii−i3−33−300000000
χ392-2-22002-2-220022-2-20000-22-222-2-22200-2-22000000000000002-2-22000000000000
χ402-2-22002-2-220022-2-20000-22-22-222-2200-2-2200000000000000-222-2000000000000
χ412-2-22002-2-2200-1211−i3i3i3−i3-22-2-12-2-22-10011-1−i3i3i3−i30000000000-111-1−i3i3i3−i300000000
χ422-2-22002-2-2200-1211−i3i3i3−i3-22-2-1-222-2-10011-1−i3i3i3−i300000000001-1-11i3−i3−i3i300000000
χ432-2-22002-2-2200-1211i3−i3−i3i3-22-2-12-2-22-10011-1i3−i3−i3i30000000000-111-1i3−i3−i3i300000000
χ442-2-22002-2-2200-1211i3−i3−i3i3-22-2-1-222-2-10011-1i3−i3−i3i300000000001-1-11−i3i3i3−i300000000
χ45444444444444-2-2-2-2-2-2-2-2-2-2-2-200001-2-2111111100000000000000000000000000
χ464444-4-44444-4-4-2-2-2-22222-2-2-2-20000122111-1-1-1-100000000000000000000000000
χ4744-4-44-444-4-44-4-2-2-22-2-22222-2200001-221-1-111-1-100000000000000000000000000
χ4844-4-4-4444-4-4-44-2-2-2222-2-222-22000012-21-1-1-1-11100000000000000000000000000
χ494-44-4004-44-4004-2-440000-222-40000-2002-22000000000000000000000000000000
χ504-44-4004-44-400-2-22-2−2i32i3−2i32i3-22220000100-11-1i3−i3i3−i300000000000000000000000000
χ514-44-4004-44-400-2-22-22i3−2i32i3−2i3-22220000100-11-1−i3i3−i3i300000000000000000000000000
χ524-4-44004-4-44004-2-4-400002-2240000-20022-2000000000000000000000000000000
χ534-4-44004-4-4400-2-222−2i32i32i3−2i32-22-20000100-1-11i3−i3−i3i300000000000000000000000000
χ544-4-44004-4-4400-2-2222i3−2i3−2i32i32-22-20000100-1-11−i3i3i3−i300000000000000000000000000
χ55666666-3-3-3-3-3-30000000000000000000000000000002200220000000000-1-1-1-100
χ56666666-3-3-3-3-3-3000000000000000000000000000000-2-200-2-20000000000111100
χ576666-6-6-3-3-3-3330000000000000000000000000000002200-2-2000000000011-1-100
χ586666-6-6-3-3-3-333000000000000000000000000000000-2-200220000000000-1-11100
χ5966-6-66-6-3-333-330000000000000000000000000000002i−2i002i−2i0000000000−ii−ii00
χ6066-6-66-6-3-333-33000000000000000000000000000000−2i2i00−2i2i0000000000i−ii−i00
χ6166-6-6-66-3-3333-30000000000000000000000000000002i−2i00−2i2i0000000000i−i−ii00
χ6266-6-6-66-3-3333-3000000000000000000000000000000−2i2i002i−2i0000000000−iii−i00
χ6312-1212-1200-66-66000000000000000000000000000000000000000000000000000000
χ6412-12-121200-666-6000000000000000000000000000000000000000000000000000000

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