Finite Group Databasebeta

← Group #11797976

Character table — Group #11797976

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222224444444444444444444488888888888888888888888824242424242424243636363648484848484848487272
order12233446636668812121212121224242424242424246121616242424244848484848484848484848484848484822244488448866612121224241616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-11-1-1111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-111-111-1-1-1-1
χ71111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-11-1-111-1-1
χ81111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ911-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−ii−ii−ii−i11-1-1i−ii−i1-1
χ1011-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i1-1-11−iii−i−ii−ii-11-11−iii−i-11
χ1111-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i-111-1i−i−ii−ii−ii1-11-1i−i−ii-11
χ1211-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i-11-11−ii−iii−ii−i-1-111−ii−ii1-1
χ1311-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii−ii−ii−ii11-1-1−ii−ii1-1
χ1411-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii1-1-11i−i−iii−ii−i-11-11i−i−ii-11
χ1511-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii-111-1−iii−ii−ii−i1-11-1−iii−i-11
χ1611-1111-1111-11-1-11-11111-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii-11-11i−ii−i−ii−ii-1-111i−ii−i1-1
χ172222222222222-2-2222222-2-2-2-2-2-2-2-22200-2-2-2-200000000000000000000000022-2-20000000000
χ182222222222222-2-2222222-2-2-2-2-2-2-2-22200-2-2-2-2000000000000000000000000-2-2220000000000
χ192222-122-12-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200002200000-1-1000-1-100
χ202222-122-12-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-20000-2-200000110001100
χ212222-122-12-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-2111111220000-2-200000-1-10001100
χ222222-122-12-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-2111111-2-20000220000011000-1-100
χ23222-12222-1-12-1-122-12-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1002222000000-100-1-1-10000
χ24222-12222-1-12-1-122-12-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-2-2-20000001001110000
χ25222-12222-1-12-1-122-12-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-211110022-2-2000000-100-1110000
χ26222-12222-1-12-1-122-12-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-2111100-2-2220000001001-1-10000
χ2722-2222-2222-22-22-2-22222-222222222-2-200-2-2-2-20000000000000000000000002i−2i−2i2i0000000000
χ2822-2222-2222-22-22-2-22222-222222222-2-200-2-2-2-2000000000000000000000000−2i2i2i−2i0000000000
χ2922-22-12-2-12-11-1-2-22-2-12-1-11-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii2-200002i−2i00000-11000−ii00
χ3022-22-12-2-12-11-1-2-22-2-12-1-11-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii-220000−2i2i000001-1000i−i00
χ3122-22-12-2-12-11-1-2-22-2-12-1-11-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i2-20000−2i2i00000-11000i−i00
χ3222-22-12-2-12-11-1-2-22-2-12-1-11-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i-2200002i−2i000001-1000−ii00
χ3322-2-122-22-1-1-2-11-2212-1-1-1-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii002-22i−2i000000-1001−ii0000
χ3422-2-122-22-1-1-2-11-2212-1-1-1-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00-22−2i2i000000100-1i−i0000
χ3522-2-122-22-1-1-2-11-2212-1-1-1-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i002-2−2i2i000000-1001i−i0000
χ3622-2-122-22-1-1-2-11-2212-1-1-1-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00-222i−2i000000100-1−ii0000
χ3744444-4-444444400-4-4-4-4-4-4000000004-400000000000000000000000000000000000000000000
χ384444-244-24-2-2-24-4-44-24-2-2-2-4-4222222-2-200-422200000000000000000000000000000000000000
χ394444-2-4-4-24-2-2-2400-42-422200000000-22000000006−666−6−6006−666−6−60000000000000000000000
χ404444-2-4-4-24-2-2-2400-42-422200000000-2200000000−66−6−66600−66−6−6660000000000000000000000
χ41444-24444-2-24-2-2-4-4-24-2-2-2422-4-42222-2-2002-42200000000000000000000000000000000000000
χ42444-24-4-44-2-24-2-2002-4222-400000000-22000000i6−i600i6−i6i6−i6i6−i600i6−i6i6−i60000000000000000000000
χ43444-24-4-44-2-24-2-2002-4222-400000000-22000000−i6i600−i6i6−i6i6−i6i600−i6i6−i6i60000000000000000000000
χ44444-2-244-2-21-21-244-2-2-211-2-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-211110000000000000000000000
χ45444-2-244-2-21-21-244-2-2-211-2-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-10000000000000000000000
χ46444-2-244-2-21-21-2-4-4-2-2-211-22222-1-1-1-1110022-1-100003i−3i−3i3i00003i−3i−3i3i0000000000000000000000
χ47444-2-244-2-21-21-2-4-4-2-2-211-22222-1-1-1-1110022-1-10000−3i3i3i−3i0000−3i3i3i−3i0000000000000000000000
χ48444-2-2-4-4-2-21-21-200222-1-1200003i3i−3i−3i1-100003i−3ii6−i66−6−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13i6−i66−6−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ130000000000000000000000
χ49444-2-2-4-4-2-21-21-200222-1-1200003i3i−3i−3i1-100003i−3i−i6i6−66ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13−i6i6−66ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ130000000000000000000000
χ50444-2-2-4-4-2-21-21-200222-1-120000−3i−3i3i3i1-10000−3i3ii6−i6−66−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23i6−i6−66−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ230000000000000000000000
χ51444-2-2-4-4-2-21-21-200222-1-120000−3i−3i3i3i1-10000−3i3i−i6i66−6ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23−i6i66−6ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ230000000000000000000000
χ5244-444-44444-44-4004-4-4-4-4400000000-4400000000000000000000000000000000000000000000
χ5344-44-24-4-24-22-2-44-4-4-24-2-2244-2-2-2-2-2-22200-422200000000000000000000000000000000000000
χ5444-44-2-44-24-22-2-40042-422-2000000002-200000000i6−i6i6i6−i6−i600−i6i6−i6−i6i6i60000000000000000000000
χ5544-44-2-44-24-22-2-40042-422-2000000002-200000000−i6i6−i6−i6i6i600i6−i6i6i6−i6−i60000000000000000000000
χ5644-4-244-44-2-2-4-224-424-2-2-2-4-2-244-2-2-2-222002-42200000000000000000000000000000000000000
χ5744-4-24-444-2-2-4-2200-2-42224000000002-20000006−6006−66−6−6600−66−660000000000000000000000
χ5844-4-24-444-2-2-4-2200-2-42224000000002-2000000−6600−66−666−6006−66−60000000000000000000000
χ5944-4-2-24-4-2-212124-42-2-2112-2-2-2-21111-1-10022-1-100003-3-330000-333-30000000000000000000000
χ6044-4-2-24-4-2-212124-42-2-2112-2-2-2-21111-1-10022-1-10000-333-300003-3-330000000000000000000000
χ6144-4-2-24-4-2-21212-442-2-21122222-1-1-1-1-1-14i−4i-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000
χ6244-4-2-24-4-2-21212-442-2-21122222-1-1-1-1-1-1−4i4i-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000
χ6344-4-2-2-44-2-2121200-222-1-1-200003i3i−3i−3i-110000−3i3i6−6i6−i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−66−i6i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ130000000000000000000000
χ6444-4-2-2-44-2-2121200-222-1-1-200003i3i−3i−3i-110000−3i3i−66−i6i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ136−6i6−i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ130000000000000000000000
χ6544-4-2-2-44-2-2121200-222-1-1-20000−3i−3i3i3i-1100003i−3i6−6−i6i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−66i6−i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ230000000000000000000000
χ6644-4-2-2-44-2-2121200-222-1-1-20000−3i−3i3i3i-1100003i−3i−66i6−i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ236−6−i6i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ230000000000000000000000
χ678-808800-8-880-8000000000000000000000000000000000000000000000000000000000000000
χ688-808-4004-8-404000000000002i6−2i62i6−2i62i6−2i60000000000000000000000000000000000000000000000
χ698-808-4004-8-40400000000000−2i62i6−2i62i6−2i62i60000000000000000000000000000000000000000000000
χ708-80-4800-84-40400000000026−260026−26−26260000000000000000000000000000000000000000000000
χ718-80-4800-84-404000000000−262600−262626−260000000000000000000000000000000000000000000000
χ728-80-4-4004420-20000006i−6i026−262i6−2i6−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000000000000000
χ738-80-4-4004420-20000006i−6i0−2626−2i62i62ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000000000000000
χ748-80-4-4004420-2000000−6i6i026−26−2i62i62ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000000000000000
χ758-80-4-4004420-2000000−6i6i0−26262i6−2i6−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.