Finite Group Databasebeta

← Group #11721302

Character table — Group #11721302

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111122226666666612121212181818181818181818181818181818181818111122226666666612121212181818181818181818181818181818181818
order1222366633666666366644444412121212121212121212121222226666666666666666444444121212121212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ51-11-11-1-111111-1-1-1-111-1-11-1i−ii−i11-1-1ii−i−iii−i−i1-11-11-1-111111-1-1-1-111-1-11-1i−ii−i11-1-1ii−i−iii−i−i
χ61-11-11-1-111111-1-1-1-111-1-11-1−ii−ii11-1-1−i−iii−i−iii1-11-11-1-111111-1-1-1-111-1-11-1−ii−ii11-1-1−i−iii−i−iii
χ71-11-11-1-111111-1-1-1-111-1-1-11i−i−ii-1-111ii−i−i−i−iii1-11-11-1-111111-1-1-1-111-1-1-11i−i−ii-1-111ii−i−i−i−iii
χ81-11-11-1-111111-1-1-1-111-1-1-11−iii−i-1-111−i−iiiii−i−i1-11-11-1-111111-1-1-1-111-1-1-11−iii−i-1-111−i−iiiii−i−i
χ9222222222-12-12-12-1-1-1-1-100002200000000-1-1-1-1222222222-12-12-12-1-1-1-1-100002200000000-1-1-1-1
χ10222222222-12-12-12-1-1-1-1-10000-2-2000000001111222222222-12-12-12-1-1-1-1-10000-2-2000000001111
χ1122222222-12-12-12-12-1-1-1-10022000000-1-1-1-1000022222222-12-12-12-12-1-1-1-10022000000-1-1-1-10000
χ1222222222-12-12-12-12-1-1-1-100-2-20000001111000022222222-12-12-12-12-1-1-1-100-2-200000011110000
χ1322-2-222-2-222-2-222-2-22-22-200000000000000000022-2-222-2-222-2-222-2-22-22-2000000000000000000
χ1422-2-222-2-22-1-212-1-21-11-11000000000000003−33−322-2-222-2-22-1-212-1-21-11-11000000000000003−33−3
χ1522-2-222-2-22-1-212-1-21-11-1100000000000000−33−3322-2-222-2-22-1-212-1-21-11-1100000000000000−33−33
χ1622-2-222-2-2-121-2-121-2-11-1100000000003−33−3000022-2-222-2-2-121-2-121-2-11-1100000000003−33−30000
χ1722-2-222-2-2-121-2-121-2-11-110000000000−33−33000022-2-222-2-2-121-2-121-2-11-110000000000−33−330000
χ182-22-22-2-222-12-1-21-21-1-11100002i−2i00000000−i−iii2-22-22-2-222-12-1-21-21-1-11100002i−2i00000000−i−iii
χ192-22-22-2-222-12-1-21-21-1-1110000−2i2i00000000ii−i−i2-22-22-2-222-12-1-21-21-1-1110000−2i2i00000000ii−i−i
χ202-22-22-2-22-12-121-21-2-1-111002i−2i000000−i−iii00002-22-22-2-22-12-121-21-2-1-111002i−2i000000−i−iii0000
χ212-22-22-2-22-12-121-21-2-1-11100−2i2i000000ii−i−i00002-22-22-2-22-12-121-21-2-1-11100−2i2i000000ii−i−i0000
χ222-2-222-22-222-2-2-2-2222-2-220000000000000000002-2-222-22-222-2-2-2-2222-2-22000000000000000000
χ232-2-222-22-22-1-21-212-1-111-100000000000000−i3i3i3−i32-2-222-22-22-1-21-212-1-111-100000000000000−i3i3i3−i3
χ242-2-222-22-22-1-21-212-1-111-100000000000000i3−i3−i3i32-2-222-22-22-1-21-212-1-111-100000000000000i3−i3−i3i3
χ252-2-222-22-2-121-21-2-12-111-10000000000−i3i3i3−i300002-2-222-22-2-121-21-2-12-111-10000000000−i3i3i3−i30000
χ262-2-222-22-2-121-21-2-12-111-10000000000i3−i3−i3i300002-2-222-22-2-121-21-2-12-111-10000000000i3−i3−i3i30000
χ2744444444-2-2-2-2-2-2-2-2111100000000000000000044444444-2-2-2-2-2-2-2-21111000000000000000000
χ2844-4-444-4-4-2-222-2-2221-11-100000000000000000044-4-444-4-4-2-222-2-2221-11-1000000000000000000
χ294-44-44-4-44-2-2-2-2222211-1-10000000000000000004-44-44-4-44-2-2-2-2222211-1-1000000000000000000
χ304-4-444-44-4-2-22222-2-21-1-110000000000000000004-4-444-44-4-2-22222-2-21-1-11000000000000000000
χ316666-3-3-3-3000000000000220000-1-1-1-1000000006666-3-3-3-3000000000000220000-1-1-1-100000000
χ326666-3-3-3-3000000000000-2-200001111000000006666-3-3-3-3000000000000-2-20000111100000000
χ3366-6-6-3-3330000000000000000003−33−30000000066-6-6-3-3330000000000000000003−33−300000000
χ3466-6-6-3-333000000000000000000−33−330000000066-6-6-3-333000000000000000000−33−3300000000
χ356-66-6-333-30000000000002-20000-1-111000000006-66-6-333-30000000000002-20000-1-11100000000
χ366-66-6-333-3000000000000-22000011-1-1000000006-66-6-333-3000000000000-22000011-1-100000000
χ376-6-66-33-330000000000000000003−3−33000000006-6-66-33-330000000000000000003−3−3300000000
χ386-6-66-33-33000000000000000000−333−3000000006-6-66-33-33000000000000000000−333−300000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ401111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ4111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ4211111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ431-11-11-1-111111-1-1-1-111-1-11-1i−ii−i11-1-1ii−i−iii−i−i-11-11-111-1-1-1-1-11111-1-111-11−ii−ii-1-111−i−iii−i−iii
χ441-11-11-1-111111-1-1-1-111-1-11-1−ii−ii11-1-1−i−iii−i−iii-11-11-111-1-1-1-1-11111-1-111-11i−ii−i-1-111ii−i−iii−i−i
χ451-11-11-1-111111-1-1-1-111-1-1-11i−i−ii-1-111ii−i−i−i−iii-11-11-111-1-1-1-1-11111-1-1111-1−iii−i11-1-1−i−iiiii−i−i
χ461-11-11-1-111111-1-1-1-111-1-1-11−iii−i-1-111−i−iiiii−i−i-11-11-111-1-1-1-1-11111-1-1111-1i−i−ii11-1-1ii−i−i−i−iii
χ47222222222-12-12-12-1-1-1-1-100002200000000-1-1-1-1-2-2-2-2-2-2-2-2-21-21-21-2111110000-2-2000000001111
χ48222222222-12-12-12-1-1-1-1-10000-2-2000000001111-2-2-2-2-2-2-2-2-21-21-21-21111100002200000000-1-1-1-1
χ4922222222-12-12-12-12-1-1-1-10022000000-1-1-1-10000-2-2-2-2-2-2-2-21-21-21-21-2111100-2-200000011110000
χ5022222222-12-12-12-12-1-1-1-100-2-200000011110000-2-2-2-2-2-2-2-21-21-21-21-211110022000000-1-1-1-10000
χ5122-2-222-2-222-2-222-2-22-22-2000000000000000000-2-222-2-222-2-222-2-222-22-22000000000000000000
χ5222-2-222-2-22-1-212-1-21-11-11000000000000003−33−3-2-222-2-222-212-1-212-11-11-100000000000000−33−33
χ5322-2-222-2-22-1-212-1-21-11-1100000000000000−33−33-2-222-2-222-212-1-212-11-11-1000000000000003−33−3
χ5422-2-222-2-2-121-2-121-2-11-1100000000003−33−30000-2-222-2-2221-2-121-2-121-11-10000000000−33−330000
χ5522-2-222-2-2-121-2-121-2-11-110000000000−33−330000-2-222-2-2221-2-121-2-121-11-100000000003−33−30000
χ562-22-22-2-222-12-1-21-21-1-11100002i−2i00000000−i−iii-22-22-222-2-21-212-12-111-1-10000−2i2i00000000ii−i−i
χ572-22-22-2-222-12-1-21-21-1-1110000−2i2i00000000ii−i−i-22-22-222-2-21-212-12-111-1-100002i−2i00000000−i−iii
χ582-22-22-2-22-12-121-21-2-1-111002i−2i000000−i−iii0000-22-22-222-21-21-2-12-1211-1-100−2i2i000000ii−i−i0000
χ592-22-22-2-22-12-121-21-2-1-11100−2i2i000000ii−i−i0000-22-22-222-21-21-2-12-1211-1-1002i−2i000000−i−iii0000
χ602-2-222-22-222-2-2-2-2222-2-22000000000000000000-222-2-22-22-2-22222-2-2-222-2000000000000000000
χ612-2-222-22-22-1-21-212-1-111-100000000000000−i3i3i3−i3-222-2-22-22-212-12-1-211-1-1100000000000000i3−i3−i3i3
χ622-2-222-22-22-1-21-212-1-111-100000000000000i3−i3−i3i3-222-2-22-22-212-12-1-211-1-1100000000000000−i3i3i3−i3
χ632-2-222-22-2-121-21-2-12-111-10000000000−i3i3i3−i30000-222-2-22-221-2-12-121-21-1-110000000000i3−i3−i3i30000
χ642-2-222-22-2-121-21-2-12-111-10000000000i3−i3−i3i30000-222-2-22-221-2-12-121-21-1-110000000000−i3i3i3−i30000
χ6544444444-2-2-2-2-2-2-2-21111000000000000000000-4-4-4-4-4-4-4-422222222-1-1-1-1000000000000000000
χ6644-4-444-4-4-2-222-2-2221-11-1000000000000000000-4-444-4-44422-2-222-2-2-11-11000000000000000000
χ674-44-44-4-44-2-2-2-2222211-1-1000000000000000000-44-44-444-42222-2-2-2-2-1-111000000000000000000
χ684-4-444-44-4-2-22222-2-21-1-11000000000000000000-444-4-44-4422-2-2-2-222-111-1000000000000000000
χ696666-3-3-3-3000000000000220000-1-1-1-100000000-6-6-6-63333000000000000-2-20000111100000000
χ706666-3-3-3-3000000000000-2-20000111100000000-6-6-6-63333000000000000220000-1-1-1-100000000
χ7166-6-6-3-3330000000000000000003−33−300000000-6-66633-3-3000000000000000000−33−3300000000
χ7266-6-6-3-333000000000000000000−33−3300000000-6-66633-3-30000000000000000003−33−300000000
χ736-66-6-333-30000000000002-20000-1-11100000000-66-663-3-33000000000000-22000011-1-100000000
χ746-66-6-333-3000000000000-22000011-1-100000000-66-663-3-330000000000002-20000-1-11100000000
χ756-6-66-33-330000000000000000003−3−3300000000-666-63-33-3000000000000000000−333−300000000
χ766-6-66-33-33000000000000000000−333−300000000-666-63-33-30000000000000000003−3−3300000000

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