Finite Group Databasebeta

← Group #11798617

Character table — Group #11798617

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size112222222444444444444444488888888888888881212121212121212121212121616161616242424242424242424242424484848144144
order1223366662234446666121212121212266666612121212121212121244441212121212121212666662444661212121212128242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111-1-111111-1-1-1-111-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1111-11111-1-111-1-1-11-1
χ6111111111111-1-111111-1-1-1-111-111-1-111111-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-11-1-1-111-1-1-1-1111-11
χ7111111111111-1-111111-1-1-1-111-111-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-111-1111-1-11111-1-1-1-11
χ8111111111111-1-111111-1-1-1-111-111-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-11-1-1-1-111-1-11111-1
χ92222222222-2200-222220000-2-202-2002-2-2-2-200000000220000222202-200000-20000-2-20000000
χ102222222222-2200-222220000-2-202-2002-2-2-2-200000000-2-20000-2-2-2-202-20000020000220000000
χ11222222222-22200-222220000-2-20-2200-22-2-2-20000002200222200000-220000-2000-2-2000000000
χ12222222222-22200-222220000-2-20-2200-22-2-2-2000000-2-200-2-2-2-200000-220000200022000000000
χ13222222222-2-222222222222222-2-2-2-2-2-2-2222222222000000000000-2-2-2-2-200000000000000000
χ14222222222-2-22-2-222222-2-2-2-2222-2-222-2-2222-2-2-2-2-2-20000000000002-2-22200000000000000000
χ152222-122-1222-1222-1-1-1-12222-1-122222-1-12-1-1-1-1-1-1-1-1000000000000-1-1-1-1-12200-1-10000-1-12-1-100
χ162222-122-1222-1222-1-1-1-12222-1-122222-1-12-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-2-20011000011-21100
χ172222-122-1222-1-2-22-1-1-1-1-2-2-2-2-1-1-222-2-2-1-12-1-11111110000000000001-1-1112200-1-10000-1-1-21100
χ182222-122-1222-1-2-22-1-1-1-1-2-2-2-2-1-1-222-2-2-1-12-1-11111110000000000001-1-111-2-200110000112-1-100
χ192222-122-12-2-2-1222-1-1-1-12222-1-1-2-2-2-2-2112-1-1-1-1-1-1-1-1000000000000111110000−i3i30000−i3i30−i3i300
χ202222-122-12-2-2-1222-1-1-1-12222-1-1-2-2-2-2-2112-1-1-1-1-1-1-1-1000000000000111110000i3−i30000i3−i30i3−i300
χ212222-122-12-2-2-1-2-22-1-1-1-1-2-2-2-2-1-12-2-222112-1-1111111000000000000-111-1-10000−i3i30000−i3i30i3−i300
χ222222-122-12-2-2-1-2-22-1-1-1-1-2-2-2-2-1-12-2-222112-1-1111111000000000000-111-1-10000i3−i30000i3−i30−i3i300
χ23222-12-1-12-122-12222-1-1-1-1-1-1-1222-1-1-1-122-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-1002200-1-1-1-10000000
χ24222-12-1-12-122-12222-1-1-1-1-1-1-1222-1-1-1-122-1-1-122-1-1-1-1-2-2-2-2111111112-1-1-1-100-2-20011110000000
χ25222-12-1-12-122-1-2-222-1-1-1111122-2-1-11122-1-1-1-2-2111122-2-2-1-1-1-11111-2-1-111002-200-1-1110000000
χ26222-12-1-12-122-1-2-222-1-1-1111122-2-1-11122-1-1-1-2-21111-2-2221111-1-1-1-1-2-1-11100-220011-1-10000000
χ27222-12-1-12-12-2-100-22-1-1-1−i3−i3i3i3-2-20-11−i3i32-211100−i3−i3i3i30022−i3−i3i3i3-1-1-1-10-11−i3i3000-200−i3i3110000000
χ28222-12-1-12-12-2-100-22-1-1-1−i3−i3i3i3-2-20-11−i3i32-211100−i3−i3i3i300-2-2i3i3−i3−i311110-11−i3i3000200i3−i3-1-10000000
χ29222-12-1-12-12-2-100-22-1-1-1i3i3−i3−i3-2-20-11i3−i32-211100i3i3−i3−i30022i3i3−i3−i3-1-1-1-10-11i3−i3000-200i3−i3110000000
χ30222-12-1-12-12-2-100-22-1-1-1i3i3−i3−i3-2-20-11i3−i32-211100i3i3−i3−i300-2-2−i3−i3i3i311110-11i3−i3000200−i3i3-1-10000000
χ31222-12-1-12-1-22-100-22-1-1-1−i3−i3i3i3-2-201-1i3−i3-2211100−i3−i3i3i32200-1-1-1-1−i3−i3i3i301-1i3−i300-200011−i3i30000000
χ32222-12-1-12-1-22-100-22-1-1-1−i3−i3i3i3-2-201-1i3−i3-2211100−i3−i3i3i3-2-2001111i3i3−i3−i301-1i3−i3002000-1-1i3−i30000000
χ33222-12-1-12-1-22-100-22-1-1-1i3i3−i3−i3-2-201-1−i3i3-2211100i3i3−i3−i32200-1-1-1-1i3i3−i3−i301-1−i3i300-200011i3−i30000000
χ34222-12-1-12-1-22-100-22-1-1-1i3i3−i3−i3-2-201-1−i3i3-2211100i3i3−i3−i3-2-2001111−i3−i3i3i301-1−i3i3002000-1-1−i3i30000000
χ35222-12-1-12-1-2-2-12222-1-1-1-1-1-1-122-21111-2-2-1-1-122-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-21111000000i3−i3i3−i30000000
χ36222-12-1-12-1-2-2-12222-1-1-1-1-1-1-122-21111-2-2-1-1-122-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-21111000000−i3i3−i3i30000000
χ37222-12-1-12-1-2-2-1-2-222-1-1-1111122211-1-1-2-2-1-1-1-2-211110000−i3−i3i3i3i3i3−i3−i3211-1-1000000i3−i3−i3i30000000
χ38222-12-1-12-1-2-2-1-2-222-1-1-1111122211-1-1-2-2-1-1-1-2-211110000i3i3−i3−i3−i3−i3i3i3211-1-1000000−i3i3i3−i30000000
χ394444-244-244-4-200-4-2-2-2-200002204-400-22-4220000000000000000000-220000000000000000000
χ404444-244-24-44-200-4-2-2-2-20000220-44002-2-42200000000000000000002-20000000000000000000
χ41444-2-2-2-2-2-2441444-2111-2-2-2-2-2-24-2-2-2-2-2-2-211-2-21111000000000000-2111100000000000000000
χ42444-2-2-2-2-2-2441-4-44-21112222-2-2-4-2-222-2-2-21122-1-1-1-1000000000000211-1-100000000000000000
χ43444-2-2-2-2-2-24-4100-4-2111−2i3−2i32i32i3220-22−2i32i3-222-1-100i3i3−i3−i300000000000001-1i3−i300000000000000000
χ44444-2-2-2-2-2-24-4100-4-21112i32i3−2i3−2i3220-222i3−2i3-222-1-100−i3−i3i3i300000000000001-1−i3i300000000000000000
χ45444-2-2-2-2-2-2-44100-4-2111−2i3−2i32i32i32202-22i3−2i32-22-1-100i3i3−i3−i30000000000000-11−i3i300000000000000000
χ46444-2-2-2-2-2-2-44100-4-21112i32i3−2i3−2i32202-2−2i32i32-22-1-100−i3−i3i3i30000000000000-11i3−i300000000000000000
χ47444-2-2-2-2-2-2-4-41444-2111-2-2-2-2-2-2-4222222-211-2-211110000000000002-1-1-1-100000000000000000
χ48444-2-2-2-2-2-2-4-41-4-44-21112222-2-2422-2-222-21122-1-1-1-1000000000000-2-1-11100000000000000000
χ4944-444-4-444004000-44-4-40000000000000000000000000000000000000002-200220000-2-200000
χ5044-444-4-444004000-44-4-4000000000000000000000000000000000000000-2200-2-200002200000
χ5144-44-2-4-4-2400-20002-2220000−2i32i300000000−2i32i3000000000000000000000002-200−1−i3−1+i300001+i31−i300000
χ5244-44-2-4-4-2400-20002-2220000−2i32i300000000−2i32i300000000000000000000000-22001+i31−i30000−1−i3−1+i300000
χ5344-44-2-4-4-2400-20002-22200002i3−2i3000000002i3−2i3000000000000000000000002-200−1+i3−1−i300001−i31+i300000
χ5444-44-2-4-4-2400-20002-22200002i3−2i3000000002i3−2i300000000000000000000000-22001−i31+i30000−1+i3−1−i300000
χ554-404400-4-40042-200-4002-22-20000000000002-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ564-404400-4-40042-200-4002-22-20000000000002-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ574-404400-4-4004-2200-400-22-22000000000000-22-22-222i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ584-404400-4-4004-2200-400-22-22000000000000-22-22-22−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ594-40-24−2i32i3-4200-22-2002−2i32i3−1−i31+i3−1+i31−i30000000000002-2−1−i31+i3−1+i31−i32i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ604-40-24−2i32i3-4200-22-2002−2i32i3−1−i31+i3−1+i31−i30000000000002-2−1−i31+i3−1+i31−i3−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ614-40-24−2i32i3-4200-2-22002−2i32i31+i3−1−i31−i3−1+i3000000000000-221+i3−1−i31−i3−1+i32i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ624-40-24−2i32i3-4200-2-22002−2i32i31+i3−1−i31−i3−1+i3000000000000-221+i3−1−i31−i3−1+i3−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ634-40-242i3−2i3-4200-22-20022i3−2i3−1+i31−i3−1−i31+i30000000000002-2−1+i31−i3−1−i31+i32i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ644-40-242i3−2i3-4200-22-20022i3−2i3−1+i31−i3−1−i31+i30000000000002-2−1+i31−i3−1−i31+i3−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ654-40-242i3−2i3-4200-2-220022i3−2i31−i3−1+i31+i3−1−i3000000000000-221−i3−1+i31+i3−1−i32i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ664-40-242i3−2i3-4200-2-220022i3−2i31−i3−1+i31+i3−1−i3000000000000-221−i3−1+i31+i3−1−i3−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ6788-8-48448-400-4000-8-44400000000000000000000000000000000000000000000000000000000
χ6888-8-4-444-4-400200042-2-20000−4i34i3000000002i3−2i30000000000000000000000000000000000000000
χ6988-8-4-444-4-400200042-2-200004i3−4i300000000−2i32i30000000000000000000000000000000000000000
χ708-808-4004-800-44-4004004-44-4000000000000-22-22-220000000000000000000000000000000000
χ718-808-4004-800-4-4400400-44-440000000000002-22-22-20000000000000000000000000000000000
χ728-80-4-4−4i34i3440024-400-22i3−2i3−2−2i32+2i3−2+2i32−2i3000000000000-221+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ738-80-4-4−4i34i344002-4400-22i3−2i32+2i3−2−2i32−2i3−2+2i30000000000002-2−1−i31+i3−1+i31−i30000000000000000000000000000000000
χ748-80-4-44i3−4i3440024-400-2−2i32i3−2+2i32−2i3−2−2i32+2i3000000000000-221−i3−1+i31+i3−1−i30000000000000000000000000000000000
χ758-80-4-44i3−4i344002-4400-2−2i32i32−2i3−2+2i32+2i3−2−2i30000000000002-2−1+i31−i3−1−i31+i30000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.