Finite Group Databasebeta

← Group #13165957

Character table — Group #13165957

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222668888121212121212121212121212121212121212121212121212121212121616161616161616161616161616161618182424242424242424545472727272108108108108
order122233336666666666664436664488121212121212121224242424242424242424242424242424333366666666666644121212121212121244121212122288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-11111-1-1-1-11111-1-1-1-1-1111-1-1i−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−ii−iii−i−i1-11-1
χ611-1-11111-1-1-1-11111-1-1-1-1-1111-1-1i−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1−iiiiii−i−i−i−i−ii−i−iii-11-11
χ711-1-11111-1-1-1-11111-1-1-1-1-1111-1-1−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1i−i−i−i−i−iiiiii−iii−i−i-11-11
χ811-1-11111-1-1-1-11111-1-1-1-1-1111-1-1−ii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−ii−i−iii1-11-1
χ92222222222222222222222-1-1-1-10000222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000000022-1-1-1-10000
χ102222222222222222222222-1-1-1-10000222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000-2-211110000
χ1122222-1-1-12-1-1-12-1-1-12-1-1-122222222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1002-1-1-12-1-1-10000000000
χ1222222-1-1-12-1-1-12-1-1-12-1-1-1222222-2-2-2-22-1-1-12-1-1-1-2-2111111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-100-2111-21110000000000
χ132222-12-1-1-12-1-1-12-1-1-12-1-12222222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-100-12-1-1-12-1-10000000000
χ142222-12-1-1-12-1-1-12-1-1-12-1-1222222-2-2-2-2-12-1-1-12-1-111-2-2111111-2-21111-12-1-1-12-1-1-1-122-1-1-1-1001-2111-2110000000000
χ152222-1-12-1-1-12-1-1-12-1-1-12-12222222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-100-1-12-1-1-12-10000000000
χ162222-1-12-1-1-12-1-1-12-1-1-12-1222222-2-2-2-2-1-12-1-1-12-11111-2-2111111-2-211-1-12-1-1-12-1-1-1-1-122-1-10011-2111-210000000000
χ172222-1-1-12-1-1-12-1-1-12-1-1-122222222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-12200-1-1-12-1-1-120000000000
χ182222-1-1-12-1-1-12-1-1-12-1-1-12222222-2-2-2-2-1-1-12-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-12200111-2111-20000000000
χ1922-2-22222-2-2-2-22222-2-2-2-2-22-1-11100002222-2-2-2-20000000000000000-1-1-1-1-1-1-1-1111111112i−2i000000002i−2i−i−iii0000
χ2022-2-22222-2-2-2-22222-2-2-2-2-22-1-11100002222-2-2-2-20000000000000000-1-1-1-1-1-1-1-111111111−2i2i00000000−2i2iii−i−i0000
χ2122-2-22-1-1-1-21112-1-1-1-2111-2222-2-22i−2i2i−2i2-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-12-1-1-1-2-2111111002i−i−i−i−2iiii0000000000
χ2222-2-22-1-1-1-21112-1-1-1-2111-2222-2-2−2i2i−2i2i2-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-12-1-1-1-2-211111100−2iiii2i−i−i−i0000000000
χ2322-2-2-12-1-11-211-12-1-11-211-2222-2-22i−2i2i−2i-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-1-12-1-111-2-2111100−i2i−i−ii−2iii0000000000
χ2422-2-2-12-1-11-211-12-1-11-211-2222-2-2−2i2i−2i2i-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i-12-1-1-12-1-111-2-2111100i−2iii−i2i−i−i0000000000
χ2522-2-2-1-12-111-21-1-12-111-21-2222-2-22i−2i2i−2i-1-12-111-21−i−i−i−i2i2i−i−iiiii−2i−2iii-1-12-1-1-12-11111-2-21100−i−i2i−iii−2ii0000000000
χ2622-2-2-1-12-111-21-1-12-111-21-2222-2-2−2i2i−2i2i-1-12-111-21iiii−2i−2iii−i−i−i−i2i2i−i−i-1-12-1-1-12-11111-2-21100ii−2ii−i−i2i−i0000000000
χ2722-2-2-1-1-12111-2-1-1-12111-2-2222-2-22i−2i2i−2i-1-1-12111-2−i−i−i−i−i−i2i2iiiiiii−2i−2i-1-1-12-1-1-12111111-2-200−i−i−i2iiii−2i0000000000
χ2822-2-2-1-1-12111-2-1-1-12111-2-2222-2-2−2i2i−2i2i-1-1-12111-2iiiiii−2i−2i−i−i−i−i−i−i2i2i-1-1-12-1-1-12111111-2-200iii−2i−i−i−i2i0000000000
χ2933333333333333333333-1-1000011-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000003311111111-1-1000011-1-1
χ3033333333333333333333-1-1000011-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-3-311111111110000-1-111
χ3133333333333333333333-1-10000-1-111-1-1-1-1-1-1-1-11111111111111111000000000000000033-1-1-1-1-1-1-1-1-1-10000-1-111
χ3233333333333333333333-1-10000-1-111-1-1-1-1-1-1-1-111111111111111110000000000000000-3-3-1-1-1-1-1-1-1-111000011-1-1
χ3333-3-33333-3-3-3-33333-3-3-3-31-10000i−i−ii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000003i−3iiiii−i−i−i−i−ii00001-1-11
χ3433-3-33333-3-3-3-33333-3-3-3-31-10000i−i−ii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000−3i3iiiii−i−i−i−ii−i0000-111-1
χ3533-3-33333-3-3-3-33333-3-3-3-31-10000−iii−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000003i−3i−i−i−i−iiiii−ii0000-111-1
χ3633-3-33333-3-3-3-33333-3-3-3-31-10000−iii−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−3i3i−i−i−i−iiiiii−i00001-1-11
χ3744444-2-2-24-2-2-24-2-2-24-2-2-244-2-2-2-200004-2-2-24-2-2-20000000000000000-2111-2111-2-211111100000000000000000000
χ384444-24-2-2-24-2-2-24-2-2-24-2-244-2-2-2-20000-24-2-2-24-2-200000000000000001-2111-21111-2-2111100000000000000000000
χ394444-2-24-2-2-24-2-2-24-2-2-24-244-2-2-2-20000-2-24-2-2-24-2000000000000000011-2111-211111-2-21100000000000000000000
χ404444-2-2-24-2-2-24-2-2-24-2-2-2444-2-2-2-20000-2-2-24-2-2-240000000000000000111-2111-2111111-2-200000000000000000000
χ4144-4-44-2-2-2-42224-2-2-2-4222-44-2-22200004-2-2-2-42220000000000000000-2111-211122-1-1-1-1-1-100000000000000000000
χ4244-4-4-24-2-22-422-24-2-22-422-44-2-2220000-24-2-22-42200000000000000001-2111-211-1-122-1-1-1-100000000000000000000
χ4344-4-4-2-24-222-42-2-24-222-42-44-2-2220000-2-24-222-42000000000000000011-2111-21-1-1-1-122-1-100000000000000000000
χ4444-4-4-2-2-24222-4-2-2-24222-4-44-2-2220000-2-2-24222-40000000000000000111-2111-2-1-1-1-1-1-12200000000000000000000
χ454-44-444444444-4-4-4-4-4-4-4-4001-1-1100000000000000000000000000001111-1-1-1-11-11-11-11-1000000000000−i3i3−i3i30000
χ464-44-444444444-4-4-4-4-4-4-4-4001-1-1100000000000000000000000000001111-1-1-1-11-11-11-11-1000000000000i3−i3i3−i30000
χ474-44-444444444-4-4-4-4-4-4-4-400-222-20000000000000000000000000000-2-2-2-22222-22-22-22-2200000000000000000000
χ484-44-44-2-2-24-2-2-2-4222-422200-222-200000000000000i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6-21112-1-1-1-221-11-11-100000000000000000000
χ494-44-44-2-2-24-2-2-2-4222-422200-222-200000000000000−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6-21112-1-1-1-221-11-11-100000000000000000000
χ504-44-4-24-2-2-24-2-22-4222-42200-222-2000000000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i61-211-12-1-11-1-221-11-100000000000000000000
χ514-44-4-24-2-2-24-2-22-4222-42200-222-2000000000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i61-211-12-1-11-1-221-11-100000000000000000000
χ524-44-4-2-24-2-2-24-222-4222-4200-222-2000000000000i6−i6−i6i600i6−i6i6−i6−i6i600i6−i611-21-1-12-11-11-1-221-100000000000000000000
χ534-44-4-2-24-2-2-24-222-4222-4200-222-2000000000000−i6i6i6−i600−i6i6−i6i6i6−i600−i6i611-21-1-12-11-11-1-221-100000000000000000000
χ544-44-4-2-2-24-2-2-24222-4222-400-222-2000000000000i6−i6i6−i6−i6i600i6−i6i6−i6−i6i600111-2-1-1-121-11-11-1-2200000000000000000000
χ554-44-4-2-2-24-2-2-24222-4222-400-222-2000000000000−i6i6−i6i6i6−i600−i6i6−i6i6i6−i600111-2-1-1-121-11-11-1-2200000000000000000000
χ564-4-444444-4-4-4-4-4-4-4-44444001-11-100000000000000000000000000001111-1-1-1-1-11-11-11-110000000000003−3−330000
χ574-4-444444-4-4-4-4-4-4-4-44444001-11-100000000000000000000000000001111-1-1-1-1-11-11-11-11000000000000−333−30000
χ584-4-444444-4-4-4-4-4-4-4-4444400-22-220000000000000000000000000000-2-2-2-222222-22-22-22-200000000000000000000
χ594-4-444-2-2-2-4222-42224-2-2-200-22-22000000000000006−66−66−600−66−66−66-21112-1-1-12-2-11-11-1100000000000000000000
χ604-4-444-2-2-2-4222-42224-2-2-200-22-2200000000000000−66−66−66006−66−66−6-21112-1-1-12-2-11-11-1100000000000000000000
χ614-4-44-24-2-22-4222-422-24-2-200-22-220000000000006−6006−6−66−6600−666−61-211-12-1-1-112-2-11-1100000000000000000000
χ624-4-44-24-2-22-4222-422-24-2-200-22-22000000000000−6600−666−66−6006−6−661-211-12-1-1-112-2-11-1100000000000000000000
χ634-4-44-2-24-222-4222-42-2-24-200-22-220000000000006−6−66006−6−666−600−6611-21-1-12-1-11-112-2-1100000000000000000000
χ644-4-44-2-24-222-4222-42-2-24-200-22-22000000000000−666−600−666−6−66006−611-21-1-12-1-11-112-2-1100000000000000000000
χ654-4-44-2-2-24222-4222-4-2-2-2400-22-220000000000006−66−6−6600−66−666−600111-2-1-1-12-11-11-112-200000000000000000000
χ664-4-44-2-2-24222-4222-4-2-2-2400-22-22000000000000−66−666−6006−66−6−6600111-2-1-1-12-11-11-112-200000000000000000000
χ6766666-3-3-36-3-3-36-3-3-36-3-3-3-2-2000022-2-2-2111-2111-2-2111111-2-21111110000000000000000002-1-1-12-1-1-10000000000
χ6866666-3-3-36-3-3-36-3-3-36-3-3-3-2-20000-2-222-2111-211122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000-2111-21110000000000
χ696666-36-3-3-36-3-3-36-3-3-36-3-3-2-2000022-2-21-2111-21111-2-2111111-2-21111000000000000000000-12-1-1-12-1-10000000000
χ706666-36-3-3-36-3-3-36-3-3-36-3-3-2-20000-2-2221-2111-211-1-122-1-1-1-1-1-122-1-1-1-10000000000000000001-2111-2110000000000
χ716666-3-36-3-3-36-3-3-36-3-3-36-3-2-2000022-2-211-2111-211111-2-2111111-2-211000000000000000000-1-12-1-1-12-10000000000
χ726666-3-36-3-3-36-3-3-36-3-3-36-3-2-20000-2-22211-2111-21-1-1-1-122-1-1-1-1-1-122-1-100000000000000000011-2111-210000000000
χ736666-3-3-36-3-3-36-3-3-36-3-3-36-2-2000022-2-2111-2111-2111111-2-2111111-2-2000000000000000000-1-1-12-1-1-120000000000
χ746666-3-3-36-3-3-36-3-3-36-3-3-36-2-20000-2-222111-2111-2-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000111-2111-20000000000
χ7566-6-66-3-3-3-63336-3-3-3-63332-200002i−2i−2i2i-21112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000000000000000002i−i−i−i−2iiii0000000000
χ7666-6-66-3-3-3-63336-3-3-3-63332-20000−2i2i2i−2i-21112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000−2iiii2i−i−i−i0000000000
χ7766-6-6-36-3-33-633-36-3-33-6332-200002i−2i−2i2i1-211-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000−i2i−i−ii−2iii0000000000
χ7866-6-6-36-3-33-633-36-3-33-6332-20000−2i2i2i−2i1-211-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000i−2iii−i2i−i−i0000000000
χ7966-6-6-3-36-333-63-3-36-333-632-200002i−2i−2i2i11-21-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000−i−i2i−iii−2ii0000000000
χ8066-6-6-3-36-333-63-3-36-333-632-20000−2i2i2i−2i11-21-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000000000ii−2ii−i−i2i−i0000000000
χ8166-6-6-3-3-36333-6-3-3-36333-62-200002i−2i−2i2i111-2-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000−i−i−i2iiii−2i0000000000
χ8266-6-6-3-3-36333-6-3-3-36333-62-20000−2i2i2i−2i111-2-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000000000iii−2i−i−i−i2i0000000000
χ838-88-88-4-4-48-4-4-4-8444-8444002-2-2200000000000000000000000000002-1-1-1-21112-2-11-11-1100000000000000000000
χ848-88-8-48-4-4-48-4-44-8444-844002-2-220000000000000000000000000000-12-1-11-211-112-2-11-1100000000000000000000
χ858-88-8-4-48-4-4-48-444-8444-84002-2-220000000000000000000000000000-1-12-111-21-11-112-2-1100000000000000000000
χ868-88-8-4-4-48-4-4-48444-8444-8002-2-220000000000000000000000000000-1-1-12111-2-11-11-112-200000000000000000000
χ878-8-888-4-4-4-8444-84448-4-4-4002-22-200000000000000000000000000002-1-1-1-2111-221-11-11-100000000000000000000
χ888-8-88-48-4-44-8444-844-48-4-4002-22-20000000000000000000000000000-12-1-11-2111-1-221-11-100000000000000000000
χ898-8-88-4-48-444-8444-84-4-48-4002-22-20000000000000000000000000000-1-12-111-211-11-1-221-100000000000000000000
χ908-8-88-4-4-48444-8444-8-4-4-48002-22-20000000000000000000000000000-1-1-12111-21-11-11-1-2200000000000000000000

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