Finite Group Databasebeta

← Group #72230452

Character table — Group #72230452

Order 2880.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1122222444444558888881010101010121216161616161618182020202020202424242424243636404040404040404040484848486060606060606060606060606060729090120120180180
order12334663561012122212151520303046666241530606060602444661212610101220202020121212121212121212303060602488882424242424242424102461244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1
χ3111111111111111111111111111-1111111-1-1111111111-1-1-1-1-111111111111-1-11-111-1-11111-1-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111-1111111-1-1-1-11111111-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11-1-1-111-1-1-1-11111-1-1-11-111
χ511111111111111111111111111-11111111-1-1111111-1-1-1111-1-1111111111-1-111-11-1-111-1-1-1-11111-1-1-1-11-1-1
χ611111111111111111111111111-11111111-1-1-1-11111-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-111-1111-1-11111-1-1-1-1-1-1-1-1111
χ711111111111111111111111111-1-111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ811111111111111111111111111-1-111111111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ91111111111111-1-1111111-1-1-1-1-11111111111i−i-1-1-1-111111111-1ii−i−iii−i−i1111-1-1i−ii−iii−i−iii−i−i1-1-1-1-1i−i
χ101111111111111-1-1111111-1-1-1-1-11111111111−ii-1-1-1-111111111-1−i−iii−i−iii1111-1-1−ii−ii−i−iii−i−iii1-1-1-1-1−ii
χ111111111111111-1-1111111-1-1-1-1-11-1111111-1-1i−i-1-1-1-1111-1-1-1-1-1-1ii−i−iii−i−i11-1-1-11i−i−iiii−i−i−i−iii-111-11−ii
χ121111111111111-1-1111111-1-1-1-1-11-1111111-1-1−ii-1-1-1-1111-1-1-1-1-1-1−i−iii−i−iii11-1-1-11−iii−i−i−iiiii−i−i-111-11i−i
χ131111111111111-1-1111111-1-1-1-1-1-11111111-1-1i−i-1-1-1-1-1-1-1111-1-1-1ii−i−iii−i−i-1-1111-1−iii−i−i−iiiii−i−i-1111-1−ii
χ141111111111111-1-1111111-1-1-1-1-1-11111111-1-1−ii-1-1-1-1-1-1-1111-1-1-1−i−iii−i−iii-1-1111-1i−i−iiii−i−i−i−iii-1111-1i−i
χ151111111111111-1-1111111-1-1-1-1-1-1-111111111i−i-1-1-1-1-1-1-1-1-1-111-1ii−i−iii−i−i-1-1-1-111−ii−ii−i−iii−i−iii1-1-111i−i
χ161111111111111-1-1111111-1-1-1-1-1-1-111111111−ii-1-1-1-1-1-1-1-1-1-111-1−i−iii−i−iii-1-1-1-111i−ii−iii−i−iii−i−i1-1-111−ii
χ172222-2222222-2-222-222-222-222220022-2-2-2-22-20022-2-2000000-2-2-20000000000000000000000000022-20000
χ182222-2222222-2-222-222-222-222220022-2-2-2-2-220022-2-200000022-200000000000000000000000000-2-220000
χ192222-2222222-2-2-2-2-222-2222-2-2-2-20022-2-2-2-22-200-2-222000000-2-22000000000000000000000000002-220000
χ202222-2222222-2-2-2-2-222-2222-2-2-2-20022-2-2-2-2-2200-2-22200000022200000000000000000000000000-22-20000
χ21222-12-12-12-12-1222-12-12-1222-12-120-1-1-12-1-10022-1-1-12-12200000-12-12-1-1-1-1-1-1-100202200-1-1-1-10000000-1000
χ22222-12-12-12-12-1222-12-12-1222-12-120-1-1-12-1-100-2-2-1-1-12-12200000-1-21-211111-1-10020-2-20011110000000-1000
χ23222-12-12-12-12-1222-12-12-1222-12-1-20-1-1-12-1-10022-1-1-121-2-200000-12-12-1-1-1-1-11100-20-2-200111100000001000
χ24222-12-12-12-12-1222-12-12-1222-12-1-20-1-1-12-1-100-2-2-1-1-121-2-200000-1-21-2111111100-202200-1-1-1-100000001000
χ25222-12-12-12-12-12-2-2-12-12-12-2-21-2120-1-1-12-1-1002i−2i111-2-1220000012i−i−2ii−i−iii-1-100-202i−2i00−i−iii00000001000
χ26222-12-12-12-12-12-2-2-12-12-12-2-21-2120-1-1-12-1-100−2i2i111-2-122000001−2ii2i−iii−i−i-1-100-20−2i2i00ii−i−i00000001000
χ27222-12-12-12-12-12-2-2-12-12-12-2-21-21-20-1-1-12-1-1002i−2i111-21-2-20000012i−i−2ii−i−iii110020−2i2i00ii−i−i0000000-1000
χ28222-12-12-12-12-12-2-2-12-12-12-2-21-21-20-1-1-12-1-100−2i2i111-21-2-2000001−2ii2i−iii−i−i1100202i−2i00−i−iii0000000-1000
χ2922-1222-1-12-122-122-1-1222-12-12-1202-1-12-1-1-10022-1-12-1000-12200-1-12-12-1-1-1-100-1-10200220000-1-1-1-10000-100
χ3022-1222-1-12-122-122-1-1222-12-12-1202-1-12-1-1-100-2-2-1-12-1000-12200-11-21-2111100-1-10200-2-2000011110000-100
χ3122-1222-1-12-122-122-1-1222-12-12-120-2-1-12-1-1-10022-1-12-10001-2-200-1-12-12-1-1-1-100110-200-2-2000011110000100
χ3222-1222-1-12-122-122-1-1222-12-12-120-2-1-12-1-1-100-2-2-1-12-10001-2-200-11-21-2111100110-200220000-1-1-1-10000100
χ3322-1222-1-12-122-1-2-2-1-1222-1-21-21-202-1-12-1-1-1002i−2i11-21000-122001−i2ii−2i−i−iii00-1-10-2002i−2i0000−i−iii0000100
χ3422-1222-1-12-122-1-2-2-1-1222-1-21-21-202-1-12-1-1-100−2i2i11-21000-122001i−2i−i2iii−i−i00-1-10-200−2i2i0000ii−i−i0000100
χ3522-1222-1-12-122-1-2-2-1-1222-1-21-21-20-2-1-12-1-1-1002i−2i11-210001-2-2001−i2ii−2i−i−iii00110200−2i2i0000ii−i−i0000-100
χ3622-1222-1-12-122-1-2-2-1-1222-1-21-21-20-2-1-12-1-1-100−2i2i11-210001-2-2001i−2i−i2iii−i−i001102002i−2i0000−i−iii0000-100
χ3744444444-14-144004-1-1-1-1-10000044-1-1-1-1-1-1440000004-1-14-1-1-1-1000000000-1-1-1-100000000000000-1000000
χ3844444444-14-144004-1-1-1-1-1000004-4-1-1-1-1-1-1-4-40000004-1-1-41111000000000-1-111000000000000001000000
χ3944444444-14-144004-1-1-1-1-100000-44-1-1-1-1-1-1-4-4000000-4114-1-11100000000011-1-1000000000000001000000
χ4044444444-14-144004-1-1-1-1-100000-4-4-1-1-1-1-1-144000000-411-411-1-1000000000111100000000000000-1000000
χ414444-4444-14-1-4-400-4-1-11-1-10000000-1-111114-40000000−550−5511000000000−55−5500000000000000-1000000
χ424444-4444-14-1-4-400-4-1-11-1-10000000-1-111114-400000005−505−5110000000005−55−500000000000000-1000000
χ434444-4444-14-1-4-400-4-1-11-1-10000000-1-11111-440000000−5505−5-1-1000000000−555−5000000000000001000000
χ444444-4444-14-1-4-400-4-1-11-1-10000000-1-11111-4400000005−50−55-1-10000000005−5−55000000000000001000000
χ45444-2-4-24-24-242-44424-2-4-24-44-24-200-2-22-4220000-2-22-4000000002000000000000000000000000000000000
χ46444-2-4-24-24-242-4-4-424-2-4-244-42-4200-2-22-422000022-2400000000-2000000000000000000000000000000000
χ4744-24-44-2-24-24-42442-24-44-2-4-24-2400-2-2-42220000-2-2-42000000002000000000000000000000000000000000
χ4844-24-44-2-24-24-42-4-42-24-44-242-42-400-2-2-42220000224-200000000-2000000000000000000000000000000000
χ4944-2-24-2-21414-2-2441-2-24-2-24-2-2-2-20011-2-211004411-2-2000000001-2-2-2-211110000000000000000000000000
χ5044-2-24-2-21414-2-2441-2-24-2-24-2-2-2-20011-2-21100-4-411-2-20000000012222-1-1-1-10000000000000000000000000
χ5144-2-24-2-21414-2-2-4-41-2-24-2-2-422220011-2-211004i−4i-1-12200000000-1−2i−2i2i2iii−i−i0000000000000000000000000
χ5244-2-24-2-21414-2-2-4-41-2-24-2-2-422220011-2-21100−4i4i-1-12200000000-12i2i−2i−2i−i−iii0000000000000000000000000
χ5344-2-2-4-2-214142244-1-2-2-4-2-2-4-2-2-2-2001122-1-10000112200000000-100003-33-30000000000000000000000000
χ5444-2-2-4-2-214142244-1-2-2-4-2-2-4-2-2-2-2001122-1-10000112200000000-10000-33-330000000000000000000000000
χ5544-2-2-4-2-2141422-4-4-1-2-2-4-2-242222001122-1-10000-1-1-2-200000000100003i−3i−3i3i0000000000000000000000000
χ5644-2-2-4-2-2141422-4-4-1-2-2-4-2-242222001122-1-10000-1-1-2-20000000010000−3i3i3i−3i0000000000000000000000000
χ574-4440-4-444-4-4004-40440-4-4044-4-4004-4000000004-400000000000000000000000000000000000000000000
χ584-4440-4-444-4-400-440440-4-40-4-444004-400000000-4400000000000000000000000000000000000000000000
χ594-44-202-4-242-4004-404-202-404-2-4200-2200000000-22000000000000000000000000000006−66−600000000000
χ604-44-202-4-242-4004-404-202-404-2-4200-2200000000-2200000000000000000000000000000−66−6600000000000
χ614-44-202-4-242-400-4404-202-40-424-200-22000000002-200000000000000000000000000000−i6i6i6−i600000000000
χ624-44-202-4-242-400-4404-202-40-424-200-22000000002-200000000000000000000000000000i6−i6−i6i600000000000
χ634-4-240-42-242-4004-40-240-420-242-400-2200000000-22000000000000000000000000000000000−i6i6−i6i60000000
χ644-4-240-42-242-4004-40-240-420-242-400-2200000000-22000000000000000000000000000000000i6−i6i6−i60000000
χ654-4-240-42-242-400-440-240-4202-4-2400-22000000002-20000000000000000000000000000000006−6−660000000
χ664-4-240-42-242-400-440-240-4202-4-2400-22000000002-2000000000000000000000000000000000−666−60000000
χ67888-48-48-4-2-4-2-4800-4-21-21-20000080111-21100000000-4-2-2000000000000001100000000000000000000000
χ68888-48-48-4-2-4-2-4800-4-21-21-200000-80111-2110000000042200000000000000-1-100000000000000000000000
χ69888-4-8-48-4-2-4-24-8004-2121-2000000011-12-1-1000000000−2525000000000000005−500000000000000000000000
χ70888-4-8-48-4-2-4-24-8004-2121-2000000011-12-1-100000000025−2500000000000000−5500000000000000000000000
χ7188-4888-4-4-2-4-28-400-41-2-2-21000000811-211100000000000-4-2-2000000000000011000000000000000000000
χ7288-4888-4-4-2-4-28-400-41-2-2-21000000-811-2111000000000004220000000000000-1-1000000000000000000000
χ7388-48-88-4-4-2-4-2-840041-22-210000000112-1-1-1000000000000−252500000000000005−5000000000000000000000
χ7488-48-88-4-4-2-4-2-840041-22-210000000112-1-1-100000000000025−250000000000000−55000000000000000000000
χ758-8880-8-88-2-8200000-2-20220000000-22000000000000000000−2i52i50000000000000000000000000000000000
χ768-8880-8-88-2-8200000-2-20220000000-220000000000000000002i5−2i50000000000000000000000000000000000
χ778-8-4-404428-2-8008-80-4-40440-4-444002-2000000002-200000000000000000000000000000000000000000000
χ788-8-4-404428-2-800-880-4-4044044-4-4002-200000000-2200000000000000000000000000000000000000000000
χ791616-8-816-8-84-44-4-8-800422-4220000000-1-122-1-100000000000000000000000000000000000000000000000000
χ801616-8-8-16-8-84-44-48800-4224220000000-1-1-2-21100000000000000000000000000000000000000000000000000
χ8116-1616-808-16-8-48400000-420-2400000002-2000000000000000000000000000000000000000000000000000000
χ8216-16-8160-168-8-484000002-404-200000002-2000000000000000000000000000000000000000000000000000000
χ8316-16-8-80884-4-4400000220-2-20000000-1100−3i53i500000000000000000000000000000000000000000000000000
χ8416-16-8-80884-4-4400000220-2-20000000-11003i5−3i500000000000000000000000000000000000000000000000000

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