Finite Group Databasebeta

← Group #13166034

Character table — Group #13166034

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order12223366666636662244666633366666666612121212333666666666446666666666661212448812122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1
χ41111111111111111-1-111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-111-1-1-111-11-1-111-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1111111-1-1-1-1-1-11-1i−ii−i1-1ii−i−ii−ii−ii−i
χ611-1-111-1-1-111-11-1-111-11-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1111111-1-1-1-1-1-11-1−ii−ii1-1−i−iii−ii−ii−ii
χ711-1-111-1-1-111-11-1-11-111-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1i−ii−i-11ii−i−ii−i−ii−ii
χ811-1-111-1-1-111-11-1-11-111-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-1-1-1-1-1-11111111-1−ii−ii-11−i−iii−iii−ii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1220000220000000000
χ102222222222222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111111111220000-2-20000000000
χ1122222-12-1-12-12-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-12-1-122-1-12-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-10000-1-10000000000
χ1222222-12-1-12-12-1-1-1-12222-1-1-1-1-12-1-12-1-1-122-1-12-1-12-12-1-12-1-1-122-1-122-1-122-1-1-1-122-1-1-1-10000-1-10000000000
χ1322222-12-1-12-12-1-1-1-12222-1-1-1-1-1-12-1-12-1-1-1-1222-1-12-1-12-1-12-1-1-1-12222-1-1-1-122-1-1-1-122-1-10000-1-10000000000
χ1422222-12-1-12-12-1-1-1-1-2-22211112-1-12-1-122-1-1-1-12-1-122-1-12-1-122-1-1-1-1-2-2-2-21111-2-21111-1-10000110000000000
χ1522222-12-1-12-12-1-1-1-1-2-2221111-12-1-12-1-1-122-1-12-1-12-12-1-12-1-1-122-1-1-2-211-2-21111-2-211-1-10000110000000000
χ1622222-12-1-12-12-1-1-1-1-2-2221111-1-12-1-12-1-1-1-1222-1-12-1-12-1-12-1-1-1-122-2-21111-2-21111-2-2-1-10000110000000000
χ172222-12-122-12-1-1-1-1-100220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-1-1222200-1-1-1-1-1-10000
χ182222-12-122-12-1-1-1-1-100220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000-1-1-2-2-2-2001111110000
χ1922-2-222-2-2-222-22-2-222-22-222-2-2-1-1-1-1-1-111111122-2-2-1-1-1-1-1-11111112-2-1-1-1-1-1-11111112-200002-20000000000
χ2022-2-222-2-2-222-22-2-22-222-2-2-222-1-1-1-1-1-111111122-2-2-1-1-1-1-1-1111111-22111111-1-1-1-1-1-12-20000-220000000000
χ2122-2-22-1-2112-1-2-111-12-22-2-1-1112-1-12-1-1-2-211112-11-22-1-12-1-1-2-211112-222-1-1-1-1-2-21111-110000-110000000000
χ2222-2-22-1-2112-1-2-111-12-22-2-1-111-12-1-12-111-2-2112-11-2-12-1-12-111-2-2112-2-1-122-1-111-2-211-110000-110000000000
χ2322-2-22-1-2112-1-2-111-12-22-2-1-111-1-12-1-121111-2-22-11-2-1-12-1-121111-2-22-2-1-1-1-1221111-2-2-110000-110000000000
χ2422-2-22-1-2112-1-2-111-1-222-211-1-12-1-12-1-1-2-211112-11-22-1-12-1-1-2-21111-22-2-2111122-1-1-1-1-1100001-10000000000
χ2522-2-22-1-2112-1-2-111-1-222-211-1-1-12-1-12-111-2-2112-11-2-12-1-12-111-2-211-2211-2-211-1-122-1-1-1100001-10000000000
χ2622-2-22-1-2112-1-2-111-1-222-211-1-1-1-12-1-121111-2-22-11-2-1-12-1-121111-2-2-221111-2-2-1-1-1-122-1100001-10000000000
χ2722-2-2-121-2-2-121-111-1002-20000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-111111100000000000000-112i−2i2i−2i00−i−iii−ii0000
χ2822-2-2-121-2-2-121-111-1002-20000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-111111100000000000000-11−2i2i−2i2i00ii−i−ii−i0000
χ29333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1000000000000-1-111-1-1-1-1-1-1-1-11111-1-1
χ30333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1000000000000-1-1-1-111-1-11111-1-1-1-111
χ313333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-100000000000011000000000000-1-111-1-111-1-1-1-111-1-111
χ323333333333333333-3-3-1-1-3-3-3-3000000000000-1-1-1-100000000000011000000000000-1-1-1-111111111-1-111-1-1
χ3333-3-333-3-3-333-33-3-333-3-1133-3-3000000000000-1-111000000000000-11000000000000-11i−i−ii-11−i−iiii−ii−i−ii
χ3433-3-333-3-3-333-33-3-333-3-1133-3-3000000000000-1-111000000000000-11000000000000-11−iii−i-11ii−i−i−ii−iii−i
χ3533-3-333-3-3-333-33-3-33-33-11-3-333000000000000-1-1110000000000001-1000000000000-11i−i−ii1-1−i−iiii−i−iii−i
χ3633-3-333-3-3-333-33-3-33-33-11-3-333000000000000-1-1110000000000001-1000000000000-11−iii−i1-1ii−i−i−iii−i−ii
χ374444-24-244-24-2-2-2-2-200440000-2-2-2-2-2-2-2-2-2-2-2-2-244-211111111111100000000000000-2-20000000000000000
χ384444-2-2-2-2-2-2-2-21111004400004-2-24-2-244-2-2-2-2-2-2-2-2-211-211-2-2111100000000000000110000000000000000
χ394444-2-2-2-2-2-2-2-2111100440000-24-2-24-2-2-244-2-2-2-2-2-21-211-2111-2-21100000000000000110000000000000000
χ404444-2-2-2-2-2-2-2-2111100440000-2-24-2-24-2-2-2-244-2-2-2-211-211-21111-2-200000000000000110000000000000000
χ4144-4-4-242-4-4-242-222-2004-40000-2-2-2-2-2-2222222-24-42111111-1-1-1-1-1-100000000000000-220000000000000000
χ4244-4-4-2-2222-2-221-1-11004-400004-2-24-2-2-4-42222-2-222-211-21122-1-1-1-1000000000000001-10000000000000000
χ4344-4-4-2-2222-2-221-1-11004-40000-24-2-24-222-4-422-2-2221-211-21-1-122-1-1000000000000001-10000000000000000
χ4444-4-4-2-2222-2-221-1-11004-40000-2-24-2-242222-4-4-2-22211-211-2-1-1-1-122000000000000001-10000000000000000
χ454-44-444-44-4-4-4444-4-400000000111-1-1-11-11-11-10000111-1-1-11-11-11-100−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ464-44-444-44-4-4-4444-4-400000000111-1-1-11-11-11-10000111-1-1-11-11-11-100i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ474-44-444-44-4-4-4444-4-400000000-2-2-2222-22-22-220000-2-2-2222-22-22-2200000000000000000000000000000000
χ484-44-44-2-4-22-424-2-2220000−2i32i3−2i32i311-2-1-121-11-1-22000011-2-1-121-11-1-2200−i3i3i3−i300−i3i3i3−i300000000000000000000
χ494-44-44-2-4-22-424-2-2220000−2i32i3−2i32i31-21-12-11-1-221-100001-21-12-11-1-221-100i3−i300−i3i3i3−i300−i3i3000000000000000000
χ504-44-44-2-4-22-424-2-2220000−2i32i3−2i32i3-2112-1-1-221-11-10000-2112-1-1-221-11-10000−i3i3i3−i300−i3i3i3−i3000000000000000000
χ514-44-44-2-4-22-424-2-22200002i3−2i32i3−2i311-2-1-121-11-1-22000011-2-1-121-11-1-2200i3−i3−i3i300i3−i3−i3i300000000000000000000
χ524-44-44-2-4-22-424-2-22200002i3−2i32i3−2i31-21-12-11-1-221-100001-21-12-11-1-221-100−i3i300i3−i3−i3i300i3−i3000000000000000000
χ534-44-44-2-4-22-424-2-22200002i3−2i32i3−2i3-2112-1-1-221-11-10000-2112-1-1-221-11-10000i3−i3−i3i300i3−i3−i3i3000000000000000000
χ544-44-4-2424-42-4-2-2-22200000000-2-2-2222-22-22-220000111-1-1-11-11-11-100000000000000000000006−66−6000000
χ554-44-4-2424-42-4-2-2-22200000000-2-2-2222-22-22-220000111-1-1-11-11-11-10000000000000000000000−66−66000000
χ564-4-44444-44-4-4-44-44-400000000111-1-1-1-11-11-110000111-1-1-1-11-11-1100−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3000000000000000000
χ574-4-44444-44-4-4-44-44-400000000111-1-1-1-11-11-110000111-1-1-1-11-11-1100i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3000000000000000000
χ584-4-44444-44-4-4-44-44-400000000-2-2-22222-22-22-20000-2-2-22222-22-22-200000000000000000000000000000000
χ594-4-444-242-2-42-4-22-220000−2i32i32i3−2i311-2-1-12-11-112-2000011-2-1-12-11-112-200−i3i3i3−i300i3−i3−i3i300000000000000000000
χ604-4-444-242-2-42-4-22-220000−2i32i32i3−2i31-21-12-1-112-2-1100001-21-12-1-112-2-1100i3−i300−i3i3−i3i300i3−i3000000000000000000
χ614-4-444-242-2-42-4-22-220000−2i32i32i3−2i3-2112-1-12-2-11-110000-2112-1-12-2-11-110000−i3i3i3−i300i3−i3−i3i3000000000000000000
χ624-4-444-242-2-42-4-22-2200002i3−2i3−2i32i311-2-1-12-11-112-2000011-2-1-12-11-112-200i3−i3−i3i300−i3i3i3−i300000000000000000000
χ634-4-444-242-2-42-4-22-2200002i3−2i3−2i32i31-21-12-1-112-2-1100001-21-12-1-112-2-1100−i3i300i3−i3i3−i300−i3i3000000000000000000
χ644-4-444-242-2-42-4-22-2200002i3−2i3−2i32i3-2112-1-12-2-11-110000-2112-1-12-2-11-110000i3−i3−i3i300−i3i3i3−i3000000000000000000
χ654-4-44-24-2-442-42-22-2200000000-2-2-22222-22-22-20000111-1-1-1-11-11-110000000000000000000000i6−i6−i6i6000000
χ664-4-44-24-2-442-42-22-2200000000-2-2-22222-22-22-20000111-1-1-1-11-11-110000000000000000000000−i6i6i6−i6000000
χ6766666-36-3-36-36-3-3-3-366-2-2-3-3-3-3000000000000-211-2000000000000-2-2000000000000110000110000000000
χ6866666-36-3-36-36-3-3-3-3-6-6-2-23333000000000000-211-200000000000022000000000000110000-1-10000000000
χ696666-36-366-36-3-3-3-3-300-2-200000000000000001-2-21000000000000000000000000001122-2-2001111-1-10000
χ706666-36-366-36-3-3-3-3-300-2-200000000000000001-2-210000000000000000000000000011-2-22200-1-1-1-1110000
χ7166-6-66-3-6336-3-6-333-36-6-22-3-333000000000000-21-12000000000000-220000000000001-100001-10000000000
χ7266-6-66-3-6336-3-6-333-3-66-2233-3-3000000000000-21-120000000000002-20000000000001-10000-110000000000
χ7366-6-6-363-6-6-363-333-300-2200000000000000001-22-1000000000000000000000000001-12i−2i−2i2i00ii−i−i−ii0000
χ7466-6-6-363-6-6-363-333-300-2200000000000000001-22-1000000000000000000000000001-1−2i2i2i−2i00−i−iiii−i0000
χ758-88-8-4848-84-8-4-4-44400000000222-2-2-22-22-22-20000-1-1-1111-11-11-1100000000000000000000000000000000
χ768-88-8-4-44-4444-422-2-20000000022-4-2-242-22-2-440000-1-1211-2-11-112-200000000000000000000000000000000
χ778-88-8-4-44-4444-422-2-2000000002-42-24-22-2-442-20000-12-11-21-112-2-1100000000000000000000000000000000
χ788-88-8-4-44-4444-422-2-200000000-4224-2-2-442-22-200002-1-1-2112-2-11-1100000000000000000000000000000000
χ798-8-88-48-4-884-84-44-4400000000222-2-2-2-22-22-220000-1-1-11111-11-11-100000000000000000000000000000000
χ808-8-88-4-4-44-44442-22-20000000022-4-2-24-22-224-40000-1-1211-21-11-1-2200000000000000000000000000000000
χ818-8-88-4-4-44-44442-22-2000000002-42-24-2-224-4-220000-12-11-211-1-221-100000000000000000000000000000000
χ828-8-88-4-4-44-44442-22-200000000-4224-2-24-4-22-2200002-1-1-211-221-11-100000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-6333300-4-40000000000000000222200000000000000000000000000-1-10000000000000000
χ841212-12-12-6-6666-6-663-3-3300-44000000000000000022-2-200000000000000000000000000-110000000000000000

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