Finite Group Databasebeta

← Group #72341861

Character table — Group #72341861

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size111122446666121212121212121212121212121216161616242424242424242424243232323248484848484848484848484848484848484848484848484864646464646496969696128128128128
order124424882244222244448888888888888888888836121222444444444444448888888861224242424444424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111
χ311111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ5111111-1-1111111111111-1-1-1-1-1-111-1-11111-1-1111111111-11-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1
χ6111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1
χ7111111-1-1111111111111-1-1-1-1-1-1-1-1111111-1-111111111-11-11-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111-1-111
χ8111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-11-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ911-1-1-111-1-111-11-1-1111-1-1111-1-1-1i−ii−iii−i−i1-1ii−i−i11-1-111-1-1i−ii−i1-11-1ii−i−ii−ii−iii−i−i-1111-1-11-11-1i−ii−i
χ1011-1-1-111-1-111-11-1-1111-1-1111-1-1-1i−ii−i−i−iii1-1−i−iii11-1-1-1-111−ii−ii-11-11−i−iiii−ii−i−i−iii-1111-1-1-11-11i−ii−i
χ1111-1-1-111-1-111-11-1-1111-1-1111-1-1-1−ii−iiii−i−i1-1ii−i−i11-1-1-1-111i−ii−i-11-11ii−i−i−ii−iiii−i−i-1111-1-1-11-11−ii−ii
χ1211-1-1-111-1-111-11-1-1111-1-1111-1-1-1−ii−ii−i−iii1-1−i−iii11-1-111-1-1−ii−ii1-11-1−i−iii−ii−ii−i−iii-1111-1-11-11-1−ii−ii
χ1311-1-1-11-11-111-11-1-1111-1-1-1-1-1111i−i−iiii−i−i-11ii−i−i11-1-11-1-11−ii−ii1-1-11ii−i−ii−i−ii−i−iii-11-1-1111-1-11i−i−ii
χ1411-1-1-11-11-111-11-1-1111-1-1-1-1-1111i−i−ii−i−iii-11−i−iii11-1-1-111-1i−ii−i-111-1−i−iiii−i−iiii−i−i-11-1-111-111-1i−i−ii
χ1511-1-1-11-11-111-11-1-1111-1-1-1-1-1111−iii−iii−i−i-11ii−i−i11-1-1-111-1−ii−ii-111-1ii−i−i−iii−i−i−iii-11-1-111-111-1−iii−i
χ1611-1-1-11-11-111-11-1-1111-1-1-1-1-1111−iii−i−i−iii-11−i−iii11-1-11-1-11i−ii−i1-1-11−i−iii−iii−iii−i−i-11-1-1111-1-11−iii−i
χ172222222222222222222222222222220000220000-1-1-1-1000000000000000022220000-1-1-1-1-1-10000-1-1-1-1
χ1822222222222222222222222222-2-2-2-20000220000-1-1-1-10000000000000000-2-2-2-20000-1-1-1-1-1-100001111
χ19222222-2-2222222222222-2-2-2-2-2-222-2-20000-2-20000-1-1-1-1000000000000000022-2-20000-1-111110000-1-111
χ20222222-2-2222222222222-2-2-2-2-2-2-2-2220000-2-20000-1-1-1-10000000000000000-2-2220000-1-11111000011-1-1
χ212222-2-200-22-22-2-2222-22-200000000002-22-2002-22-222220000000000002-22-200000000-2-2000000000000
χ222222-2-200-22-22-2-2222-22-20000000000-22-2200-22-222222000000000000-22-2200000000-2-2000000000000
χ2322-2-22-20022-2-2-22-222-2-2200000000002i−2i−2i2i002i−2i−2i2i22-2-20000000000002i−2i−2i2i000000002-2000000000000
χ2422-2-22-20022-2-2-22-222-2-220000000000−2i2i2i−2i00−2i2i2i−2i22-2-2000000000000−2i2i2i−2i000000002-2000000000000
χ2522-2-2-222-2-222-22-2-2222-2-2222-2-2-22i−2i2i−2i00002-20000-1-11100000000000000002i−2i2i−2i00001-1-1-1110000−ii−ii
χ2622-2-2-222-2-222-22-2-2222-2-2222-2-2-2−2i2i−2i2i00002-20000-1-1110000000000000000−2i2i−2i2i00001-1-1-1110000i−ii−i
χ2722-2-2-22-22-222-22-2-2222-2-2-2-2-22222i−2i−2i2i0000-220000-1-11100000000000000002i−2i−2i2i00001-111-1-10000−iii−i
χ2822-2-2-22-22-222-22-2-2222-2-2-2-2-2222−2i2i2i−2i0000-220000-1-1110000000000000000−2i2i2i−2i00001-111-1-10000i−i−ii
χ29333333333333-1-1-1-1-1-1-1-13-1-13-1-133331111-1-111110000111111111111-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-10000
χ30333333333333-1-1-1-1-1-1-1-13-1-13-1-13333-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111100000011110000
χ31333333333333-1-1-1-1-1-1-1-13-1-13-1-1-3-3-3-31111-1-111110000-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-100000011110000
χ32333333333333-1-1-1-1-1-1-1-13-1-13-1-1-3-3-3-3-1-1-1-1-1-1-1-1-1-100001111-1-1-1-11111111111111111000000-1-1-1-10000
χ33333333-3-33333-1-1-1-1-1-1-1-1-311-31133-3-3111111111100001-11-1-1-1-1-111-1-1-1-1-1-1-1-1111111000000-1-1110000
χ34333333-3-33333-1-1-1-1-1-1-1-1-311-31133-3-3-1-1-1-111-1-1-1-10000-11-111111-1-1111111-1-111-1-1-1-100000011-1-10000
χ35333333-3-33333-1-1-1-1-1-1-1-1-311-311-3-33311111111110000-11-11-1-1-1-1-1-111-1-1-1-111-1-1111100000011-1-10000
χ36333333-3-33333-1-1-1-1-1-1-1-1-311-311-3-333-1-1-1-111-1-1-1-100001-11-1111111-1-1111111-1-1-1-1-1-1000000-1-1110000
χ3733-3-3-333-3-333-3-111-1-1-1113-1-1-3113i−3i3i−3iii−i−i-11ii−i−i000011-1-1i−ii−i1-11-1−i−iii−ii−ii−i−iii000000-11-110000
χ3833-3-3-333-3-333-3-111-1-1-1113-1-1-3113i−3i3i−3i−i−iii-11−i−iii0000-1-111−ii−ii-11-11ii−i−i−ii−iiii−i−i0000001-11-10000
χ3933-3-3-333-3-333-3-111-1-1-1113-1-1-311−3i3i−3i3iii−i−i-11ii−i−i0000-1-111i−ii−i-11-11−i−iiii−ii−i−i−iii0000001-11-10000
χ4033-3-3-333-3-333-3-111-1-1-1113-1-1-311−3i3i−3i3i−i−iii-11−i−iii000011-1-1−ii−ii1-11-1ii−i−ii−ii−iii−i−i000000-11-110000
χ4133-3-3-33-33-333-3-111-1-1-111-3113-1-13i−3i−3i3iii−i−i1-1ii−i−i00001-1-11−ii−ii1-1-11−i−iii−iii−iii−i−i000000-111-10000
χ4233-3-3-33-33-333-3-111-1-1-111-3113-1-13i−3i−3i3i−i−iii1-1−i−iii0000-111-1i−ii−i-111-1ii−i−i−iii−i−i−iii0000001-1-110000
χ4333-3-3-33-33-333-3-111-1-1-111-3113-1-1−3i3i3i−3iii−i−i1-1ii−i−i0000-111-1−ii−ii-111-1−i−iiii−i−iiii−i−i0000001-1-110000
χ4433-3-3-33-33-333-3-111-1-1-111-3113-1-1−3i3i3i−3i−i−iii1-1−i−iii00001-1-11i−ii−i1-1-11ii−i−ii−i−ii−i−iii000000-111-10000
χ454444-4-400-44-44-4-4444-44-400000000000000000000-2-2-2-200000000000000000000000022000000000000
χ4644-4-44-40044-4-4-44-444-4-4400000000000000000000-2-222000000000000000000000000-22000000000000
χ4766666666-2-2-2-22-22-22-2-22-222-22200002222-2-2-2-2-2-20000000022-2-2000000000000000000000000000000
χ4866666666-2-2-2-22-22-22-2-22-222-2220000-2-2-2-2-2-2222200000000-2-222000000000000000000000000000000
χ4966666666-2-2-2-2-22-22-222-2-2-2-2-2-2-200000000220000000022220000-2-2-2-200000000000000000000000000
χ5066666666-2-2-2-2-22-22-222-2-2-2-2-2-2-2000000002200000000-2-2-2-20000222200000000000000000000000000
χ51666666-6-6-2-2-2-22-22-22-2-222-2-22-2-20000222222-2-2-2-200000000-2-222000000000000000000000000000000
χ52666666-6-6-2-2-2-22-22-22-2-222-2-22-2-20000-2-2-2-22222220000000022-2-2000000000000000000000000000000
χ53666666-6-6-2-2-2-2-22-22-222-222222200000000-2-2000000002-22-20000-2-22200000000000000000000000000
χ54666666-6-6-2-2-2-2-22-22-222-222222200000000-2-200000000-22-22000022-2-200000000000000000000000000
χ556666-6-6002-22-2-222-222-2-204i−4i04i−4i00002-22-200-22-220000000000000000000000002i−2i2i−2i00000000000000
χ566666-6-6002-22-2-222-222-2-204i−4i04i−4i0000-22-22002-22-2000000000000000000000000−2i2i−2i2i00000000000000
χ576666-6-6002-22-2-222-222-2-20−4i4i0−4i4i00002-22-200-22-22000000000000000000000000−2i2i−2i2i00000000000000
χ586666-6-6002-22-2-222-222-2-20−4i4i0−4i4i0000-22-22002-22-20000000000000000000000002i−2i2i−2i00000000000000
χ596666-6-600-66-6622-2-2-22-2200000000002-22-2002-22-20000000000000000-22-220000000000000000000000
χ606666-6-600-66-6622-2-2-22-220000000000-22-2200-22-2200000000000000002-22-20000000000000000000000
χ6166-6-66-60066-6-62-22-2-222-200000000002i−2i−2i2i002i−2i−2i2i0000000000000000−2i2i2i−2i0000000000000000000000
χ6266-6-66-60066-6-62-22-2-222-20000000000−2i2i2i−2i00−2i2i2i−2i00000000000000002i−2i−2i2i0000000000000000000000
χ6366-6-66-600-2-222-2-2-2-2222204i−4i0−4i4i00002i−2i−2i2i00−2i2i2i−2i000000000000000000000000-222-200000000000000
χ6466-6-66-600-2-222-2-2-2-2222204i−4i0−4i4i0000−2i2i2i−2i002i−2i−2i2i0000000000000000000000002-2-2200000000000000
χ6566-6-66-600-2-222-2-2-2-222220−4i4i04i−4i00002i−2i−2i2i00−2i2i2i−2i0000000000000000000000002-2-2200000000000000
χ6666-6-66-600-2-222-2-2-2-222220−4i4i04i−4i0000−2i2i2i−2i002i−2i−2i2i000000000000000000000000-222-200000000000000
χ6766-6-6-666-62-2-2222-2-22-22-2-2222-2-200002i2i−2i−2i-22−2i−2i2i2i000000002i−2i−2i2i000000000000000000000000000000
χ6866-6-6-666-62-2-2222-2-22-22-2-2222-2-20000−2i−2i2i2i-222i2i−2i−2i00000000−2i2i2i−2i000000000000000000000000000000
χ6966-6-6-666-62-2-22-2-222-22-22-2-2-2222000000002-20000000022-2-20000-22-2200000000000000000000000000
χ7066-6-6-666-62-2-22-2-222-22-22-2-2-2222000000002-200000000-2-22200002-22-200000000000000000000000000
χ7166-6-6-66-662-2-2222-2-22-22-22-2-2-22200002i2i−2i−2i2-2−2i−2i2i2i00000000−2i2i2i−2i000000000000000000000000000000
χ7266-6-6-66-662-2-2222-2-22-22-22-2-2-2220000−2i−2i2i2i2-22i2i−2i−2i000000002i−2i−2i2i000000000000000000000000000000
χ7366-6-6-66-662-2-22-2-222-22-22222-2-2-200000000-22000000002-2-220000-222-200000000000000000000000000
χ7466-6-6-66-662-2-22-2-222-22-22222-2-2-200000000-2200000000-222-200002-2-2200000000000000000000000000
χ7512121212-12-12004-44-44-4-44-4-44400000000000000000000000000000000000000000000000000000000000000
χ761212-12-1212-1200-4-4444444-4-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7716-1616i−16i0000000000000000000000000000000000004-44i−4i00000000000000000000000000000000000000
χ7816-1616i−16i000000000000000000000000000000000000-22−2i2i000000000000000000000000006−6i6−i600000000
χ7916-1616i−16i000000000000000000000000000000000000-22−2i2i00000000000000000000000000−66−i6i600000000
χ8016-16−16i16i0000000000000000000000000000000000004-4−4i4i00000000000000000000000000000000000000
χ8116-16−16i16i000000000000000000000000000000000000-222i−2i000000000000000000000000006−6−i6i600000000
χ8216-16−16i16i000000000000000000000000000000000000-222i−2i00000000000000000000000000−66i6−i600000000

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