Finite Group Databasebeta

← Group #13155053

Character table — Group #13155053

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size112222244444444444444444888888888888888881212121212122424242424242424242424242424243636363672727272727272216216
order1223666233336666666666663666666666666666644121212122666666661212121212122412124461212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ51111111-111111111111111-1-11-11-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1111i−i-1ii−i−ii−i
χ61111111-111111111111111-1-11-11-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1111−ii-1−i−iii−ii
χ71111111-111111111111111-1-11-11-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1111i−i-1ii−i−i−ii
χ81111111-111111111111111-1-11-11-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1111−ii-1−i−iiii−i
χ922222222222222222222222222222222222222222000000000000000000000-2-2-2-200-2000000
χ102222222-222222222222222-2-22-22-2-2-2-2-2-2-2222-2-2-2-20000000000000000000002-2-2-2002000000
χ11222-1-1-1-1222-1-1222-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-100−i3−i3i3i30−i3i300−i3−i3i3i300−i3−i3i3i3-2-211001000000
χ12222-1-1-1-1222-1-1222-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-100i3i3−i3−i30i3−i300i3i3−i3−i300i3i3−i3−i3-2-211001000000
χ13222-1-1-1-1222-1-1222-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-122-1-100-1000000
χ14222-1-1-1-1222-1-1222-1-1-1-12-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-21111-211-2-21111-2-2111122-1-100-1000000
χ15222-1-1-1-1-222-1-1222-1-1-1-12-1-1-2-2-112-2-2-21111-1-1-1111100−i3−i3i3i30i3−i300i3i3−i3−i300−i3−i3i3i32-21100-1000000
χ16222-1-1-1-1-222-1-1222-1-1-1-12-1-1-2-2-112-2-2-21111-1-1-1111100i3i3−i3−i30−i3i300−i3−i3i3i300i3i3−i3−i32-21100-1000000
χ17222-1-1-1-1-222-1-1222-1-1-1-12-1-1-2-2-112-2-2-21111-1-1-1111122-1-1-1-1-211-2-2111122-1-1-1-1-22-1-1001000000
χ18222-1-1-1-1-222-1-1222-1-1-1-12-1-1-2-2-112-2-2-21111-1-1-11111-2-211112-1-122-1-1-1-1-2-21111-22-1-1001000000
χ19444444441-2-2-21-2-2-2-2-2-2-2-2-2111411-2-2-2-2-2-211111110000000000000000000000000220-1-1-1-100
χ20444444441-2-2-21-2-2-2-2-2-2-2-2-2111411-2-2-2-2-2-211111110000000000000000000000000-2-20111100
χ2144444444-2111-2111111111-2-2-24-2-2111111-2-2-2-2-2-2-2222222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000
χ2244444444-2111-2111111111-2-2-24-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000
χ234444444-41-2-2-21-2-2-2-2-2-2-2-2-2-1-11-41-1222222111-1-1-1-100000000000000000000000002i−2i0−i−iii00
χ244444444-41-2-2-21-2-2-2-2-2-2-2-2-2-1-11-41-1222222111-1-1-1-10000000000000000000000000−2i2i0ii−i−i00
χ254444444-4-2111-211111111122-2-4-22-1-1-1-1-1-1-2-2-22222222222-2-2-2111111-1-1-1-1-1-10000000000000
χ264444444-4-2111-211111111122-2-4-22-1-1-1-1-1-1-2-2-22222-2-2-2-2-2-2222-1-1-1-1-1-11111110000000000000
χ27444-2-2-2-24-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-2-211−1−3i32−1−3i32−1+3i32−1+3i32111111122−1−i3−1−i3−1+i3−1+i32−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i320000000000000
χ28444-2-2-2-24-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i32-2-21-2-2-211−1−3i32−1−3i32−1+3i32−1+3i321111111-2-21+i31+i31−i31−i3-21+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i320000000000000
χ29444-2-2-2-24-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-2-211−1+3i32−1+3i32−1−3i32−1−3i32111111122−1+i3−1+i3−1−i3−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i320000000000000
χ30444-2-2-2-24-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i32-2-21-2-2-211−1+3i32−1+3i32−1−3i32−1−3i321111111-2-21−i31−i31+i31+i3-21−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i320000000000000
χ31444-2-2-2-2-4-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i322212-22-1-11+3i321+3i321−3i321−3i32111-1-1-1-122−1−i3−1−i3−1+i3−1+i3-21+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i320000000000000
χ32444-2-2-2-2-4-21−1−3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i321−1−3i32−1+3i322212-22-1-11+3i321+3i321−3i321−3i32111-1-1-1-1-2-21+i31+i31−i31−i32−1−i3−1+i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i320000000000000
χ33444-2-2-2-2-4-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i322212-22-1-11−3i321−3i321+3i321+3i32111-1-1-1-122−1+i3−1+i3−1−i3−1−i3-21−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i320000000000000
χ34444-2-2-2-2-4-21−1+3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i321−1+3i32−1−3i322212-22-1-11−3i321−3i321+3i321+3i32111-1-1-1-1-2-21−i31−i31+i31+i32−1+i3−1−i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i320000000000000
χ3544-44-4-4401-2-2-212-22-22-22223310-1-30000001-1-133-3-300000000000000000000000000003−33−300
χ3644-44-4-4401-2-2-212-22-22-22223310-1-30000001-1-133-3-30000000000000000000000000000−33−3300
χ3744-44-4-4401-2-2-212-22-22-2222-3-310-130000001-1-1-3-3330000000000000000000000000000−i3i3i3−i300
χ3844-44-4-4401-2-2-212-22-22-2222-3-310-130000001-1-1-3-3330000000000000000000000000000i3−i3−i3i300
χ3944-44-4-44044444-44-44-44-4-4-40040-400000004-4-400000000000000000000000000000000000000
χ4044-4-222-2044-2-24-442-22-2-42200-20-40000000-222000000000000000000000000000−2i32i3000000000
χ4144-4-222-2044-2-24-442-22-2-42200-20-40000000-2220000000000000000000000000002i3−2i3000000000
χ424-40400-404444-40-40-40-4000004000000000-40000002-22-22-20000000002-22-22-20000000000000
χ434-40400-404444-40-40-40-4000004000000000-4000000-22-22-22000000000-22-22-220000000000000
χ444-40400-40-211123-13-13-1-3-3-3−2i32i3-2000−i3i3−i3i3−i3i3200−2i32i3002-22-22-2000−i3i3−i3i3−i3i3-11-11-110000000000000
χ454-40400-40-211123-13-13-1-3-3-3−2i32i3-2000−i3i3−i3i3−i3i3200−2i32i300-22-22-22000i3−i3i3−i3i3−i31-11-11-10000000000000
χ464-40400-40-211123-13-13-1-3-3-32i3−2i3-2000i3−i3i3−i3i3−i32002i3−2i3002-22-22-2000i3−i3i3−i3i3−i3-11-11-110000000000000
χ474-40400-40-211123-13-13-1-3-3-32i3−2i3-2000i3−i3i3−i3i3−i32002i3−2i300-22-22-22000−i3i3−i3i3−i3i31-11-11-10000000000000
χ484-40-2−2i32i32044-2-2-40-4−2i322i3202i3−2i300-20000000002−2i32i300002-2−1−i31+i3−1+i31−i30000000002-2−1−i31+i3−1+i31−i30000000000000
χ494-40-2−2i32i32044-2-2-40-4−2i322i3202i3−2i300-20000000002−2i32i30000-221+i3−1−i31−i3−1+i3000000000-221+i3−1−i31−i3−1+i30000000000000
χ504-40-2−2i32i320-21−1−3i32−1+3i3223-1−3−i321+3i32−3+i321−3i32-33+i323−i32−2i32i31000−i3i33+i32−3−i32−3+i323−i32-1i3−i3i3−i33-32-2−1−i31+i3−1+i31−i3000−i3i3−3+i323−i323+i32−3−i32-111+i32−1−i321−i32−1+i320000000000000
χ514-40-2−2i32i320-21−1−3i32−1+3i3223-1−3−i321+3i32−3+i321−3i32-33+i323−i32−2i32i31000−i3i33+i32−3−i32−3+i323−i32-1i3−i3i3−i33-3-221+i3−1−i31−i3−1+i3000i3−i33−i32−3+i32−3−i323+i321-1−1−i321+i32−1+i321−i320000000000000
χ524-40-2−2i32i320-21−1−3i32−1+3i3223-1−3−i321+3i32−3+i321−3i32-33+i323−i322i3−2i31000i3−i3−3−i323+i323−i32−3+i32-1i3−i3−i3i3-332-2−1−i31+i3−1+i31−i3000i3−i33−i32−3+i32−3−i323+i32-111+i32−1−i321−i32−1+i320000000000000
χ534-40-2−2i32i320-21−1−3i32−1+3i3223-1−3−i321+3i32−3+i321−3i32-33+i323−i322i3−2i31000i3−i3−3−i323+i323−i32−3+i32-1i3−i3−i3i3-33-221+i3−1−i31−i3−1+i3000−i3i3−3+i323−i323+i32−3−i321-1−1−i321+i32−1+i321−i320000000000000
χ544-40-22i3−2i32044-2-2-40-42i32−2i320−2i32i300-200000000022i3−2i300002-2−1+i31−i3−1−i31+i30000000002-2−1+i31−i3−1−i31+i30000000000000
χ554-40-22i3−2i32044-2-2-40-42i32−2i320−2i32i300-200000000022i3−2i30000-221−i3−1+i31+i3−1−i3000000000-221−i3−1+i31+i3−1−i30000000000000
χ564-40-22i3−2i320-21−1+3i32−1−3i3223-1−3+i321−3i32−3−i321+3i32-33−i323+i32−2i32i31000−i3i3−3+i323−i323+i32−3−i32-1−i3i3i3−i3-332-2−1+i31−i3−1−i31+i3000−i3i33+i32−3−i32−3+i323−i32-111−i32−1+i321+i32−1−i320000000000000
χ574-40-22i3−2i320-21−1+3i32−1−3i3223-1−3+i321−3i32−3−i321+3i32-33−i323+i32−2i32i31000−i3i3−3+i323−i323+i32−3−i32-1−i3i3i3−i3-33-221−i3−1+i31+i3−1−i3000i3−i3−3−i323+i323−i32−3+i321-1−1+i321−i32−1−i321+i320000000000000
χ584-40-22i3−2i320-21−1+3i32−1−3i3223-1−3+i321−3i32−3−i321+3i32-33−i323+i322i3−2i31000i3−i33−i32−3+i32−3−i323+i32-1−i3i3−i3i33-32-2−1+i31−i3−1−i31+i3000i3−i3−3−i323+i323−i32−3+i32-111−i32−1+i321+i32−1−i320000000000000
χ594-40-22i3−2i320-21−1+3i32−1−3i3223-1−3+i321−3i32−3−i321+3i32-33−i323+i322i3−2i31000i3−i33−i32−3+i32−3−i323+i32-1−i3i3−i3i33-3-221−i3−1+i31+i3−1−i3000−i3i33+i32−3−i32−3+i323−i321-1−1+i321−i32−1−i321+i320000000000000
χ60888-4-4-4-482-4222-4-42222-42222-1-422-4-42222-1-1-1-1-1-1-10000000000000000000000000000000000
χ61888-4-4-4-4-82-4222-4-42222-422-2-2-142-244-2-2-2-2-1-1-111110000000000000000000000000000000000
χ6288-88-8-880-4222-4-22-22-22-2-2-200-4040000000-44400000000000000000000000000000000000000
χ6388-8-444-402-42224-4-22-224-2-266-10-2-6000000-111-3-3330000000000000000000000000000000000
χ6488-8-444-402-42224-4-22-224-2-2-6-6-10-26000000-11133-3-30000000000000000000000000000000000
χ6588-8-444-40-42−1−3i3−1+3i3-4-221+3i3−1−3i31−3i3−1+3i3-21+3i31−3i30020400000002-2-200000000000000000000000000000000000000
χ6688-8-444-40-42−1+3i3−1−3i3-4-221−3i3−1+3i31+3i3−1−3i3-21−3i31+3i30020400000002-2-200000000000000000000000000000000000000
χ678-80800-802-4-4-4-2040404000−2i32i320002i3−2i32i3−2i32i3−2i3-200−2i32i3000000000000000000000000000000000000
χ688-80800-802-4-4-4-20404040002i3−2i32000−2i32i3−2i32i3−2i32i3-2002i3−2i3000000000000000000000000000000000000
χ698-80800-80-42224-6-2-6-2-6-266600-400000000040000000000000000000000000000000000000000
χ708-80-4−4i34i3402-422-2042i3-2−2i3-20−2i32i3−2i32i3-10002i3−2i3−3−i33+i33−i3−3+i31−i3i3i3−i33-30000000000000000000000000000000000
χ718-80-4−4i34i3402-422-2042i3-2−2i3-20−2i32i32i3−2i3-1000−2i32i33+i3−3−i3−3+i33−i31−i3i3−i3i3-330000000000000000000000000000000000
χ728-80-4−4i34i340-42−1+3i3−1−3i34-6-23−i31−3i33+i31+3i36−3+i3−3−i3002000000000-22i3−2i300000000000000000000000000000000000000
χ738-80-44i3−4i3402-422-204−2i3-22i3-202i3−2i3−2i32i3-10002i3−2i33−i3−3+i3−3−i33+i31i3−i3i3−i3-330000000000000000000000000000000000
χ748-80-44i3−4i3402-422-204−2i3-22i3-202i3−2i32i3−2i3-1000−2i32i3−3+i33−i33+i3−3−i31i3−i3−i3i33-30000000000000000000000000000000000
χ758-80-44i3−4i340-42−1−3i3−1+3i34-6-23+i31+3i33−i31−3i36−3−i3−3+i3002000000000-2−2i32i300000000000000000000000000000000000000

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