Finite Group Databasebeta

← Group #72341911

Character table — Group #72341911

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size111122446666121212121212121212121212121216161616242424242424242424243232323248484848484848484848484848484848484848484848484864646464646496969696128128128128
order1222442222442222224444444422882244444444366644444444448888888888888812122424242444886666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ311111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ5111111-1-11111111-1-1111-1-1-1-11111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111
χ6111111-1-11111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111-1-11111111-1-1111-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-1-1-1
χ8111111-1-11111111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ911-1-11-11-11-11-111-11-1-11111-1-1-1-11-11-11-1ii−i−iii−i−i1-1-11i−ii−i1-1i−ii−ii−i1-1i−iii−i−iii−i−i-1111-1-1i−ii−i1-11-1
χ1011-1-11-11-11-11-111-11-1-11111-1-1-1-11-11-11-1−i−iii−i−iii1-1-11−ii−ii1-1−ii−ii−ii1-1−ii−i−iii−i−iii-1111-1-1−ii−ii1-11-1
χ1111-1-11-11-11-11-111-11-1-11111-1-1-1-1-11-111-1ii−i−iii−i−i1-1-11i−i−ii-11i−i−ii−ii-11−iiii−i−iii−i−i-11-1-111−ii−ii1-1-11
χ1211-1-11-11-11-11-111-11-1-11111-1-1-1-1-11-111-1−i−iii−i−iii1-1-11−iii−i-11−iii−ii−i-11i−i−i−iii−i−iii-11-1-111i−ii−i1-1-11
χ1311-1-11-1-111-11-111-1-11-111-1-111-1-11-1-11-11ii−i−iii−i−i1-1-11−iii−i1-1−iii−i−ii-11−iiii−i−i−i−iii-11-1-111i−i−ii-111-1
χ1411-1-11-1-111-11-111-1-11-111-1-111-1-11-1-11-11−i−iii−i−iii1-1-11i−i−ii1-1i−i−iii−i-11i−i−i−iiiii−i−i-11-1-111−iii−i-111-1
χ1511-1-11-1-111-11-111-1-11-111-1-111-1-1-111-1-11ii−i−iii−i−i1-1-11−ii−ii-11−ii−iii−i1-1i−iii−i−i−i−iii-1111-1-1−iii−i-11-11
χ1611-1-11-1-111-11-111-1-11-111-1-111-1-1-111-1-11−i−iii−i−iii1-1-11i−ii−i-11i−ii−i−ii1-1−ii−i−iiiii−i−i-1111-1-1i−i−ii-11-11
χ172222222222222222222222222222222200000000-1-1-1-1000022000000220000000000-1-1-1-1-1-10000-1-1-1-1
χ1822222222222222222222222222-2-2-2-22200000000-1-1-1-10000-2-2000000-2-20000000000-1-111110000-1-111
χ19222222-2-22222222-2-2222-2-2-2-22222-2-2-2-200000000-1-1-1-1000022000000-2-20000000000-1-11111000011-1-1
χ20222222-2-22222222-2-2222-2-2-2-222-2-222-2-200000000-1-1-1-10000-2-2000000220000000000-1-1-1-1-1-100001111
χ212222-2-20022-2-22-2-20022-20000-220000002-22-22-22-2222200000000000000002-22-20000-2-2000000000000
χ222222-2-20022-2-22-2-20022-20000-22000000-22-22-22-2222220000000000000000-22-220000-2-2000000000000
χ2322-2-22-22-22-22-222-22-2-22222-2-2-2-22-22-22-200000000-111-100002-20000002-200000000001-1-1-1110000-11-11
χ2422-2-22-22-22-22-222-22-2-22222-2-2-2-2-22-222-200000000-111-10000-22000000-2200000000001-111-1-10000-111-1
χ2522-2-22-2-222-22-222-2-22-222-2-222-2-22-2-22-2200000000-111-100002-2000000-2200000000001-111-1-100001-1-11
χ2622-2-22-2-222-22-222-2-22-222-2-222-2-2-222-2-2200000000-111-10000-220000002-200000000001-1-1-11100001-11-1
χ2722-2-2-22002-2-222-2200-22-200002-20000002i−2i−2i2i2i−2i−2i2i2-2-2200000000000000002i−2i−2i2i00002-2000000000000
χ2822-2-2-22002-2-222-2200-22-200002-2000000−2i2i2i−2i−2i2i2i−2i2-2-220000000000000000−2i2i2i−2i00002-2000000000000
χ29333333333333-1-1-133-1-1-1-1-1-1-1-1-13333-1-11111111100001111-1-1111111-1-111-1-1-1-1-1-1-1-1000000-1-1-1-10000
χ30333333333333-1-1-133-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100000011110000
χ31333333333333-1-1-133-1-1-1-1-1-1-1-1-1-3-3-3-3-1-111111111000011-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-100000011110000
χ32333333333333-1-1-133-1-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-1-1-1-1-1-1-10000-1-11111-1-11111111111111111000000-1-1-1-10000
χ33333333-3-33333-1-1-1-3-3-1-1-11111-1-133-3-311111111110000-1-111-1-1-1-111-1-111-1-1-1-1-1-11111000000-1-1110000
χ34333333-3-33333-1-1-1-3-3-1-1-11111-1-133-3-311-1-1-1-1-1-1-1-1000011-1-1-1-111-1-11111111111-1-1-1-100000011-1-10000
χ35333333-3-33333-1-1-1-3-3-1-1-11111-1-1-3-33311111111110000-1-1-1-111-1-1-1-111-1-111-1-1-1-1111100000011-1-10000
χ36333333-3-33333-1-1-1-3-3-1-1-11111-1-1-3-33311-1-1-1-1-1-1-1-100001111111111-1-1-1-1-1-11111-1-1-1-1000000-1-1110000
χ3733-3-33-33-33-33-3-1-113-31-1-1-1-111113-33-3-11ii−i−iii−i−i0000i−ii−i-11i−ii−ii−i-11i−i−i−iii−i−iii000000−ii−ii0000
χ3833-3-33-33-33-33-3-1-113-31-1-1-1-111113-33-3-11−i−iii−i−iii0000−ii−ii-11−ii−ii−ii-11−iiii−i−iii−i−i000000i−ii−i0000
χ3933-3-33-33-33-33-3-1-113-31-1-1-1-11111-33-33-11ii−i−iii−i−i0000i−i−ii1-1i−i−ii−ii1-1−ii−i−iii−i−iii000000i−ii−i0000
χ4033-3-33-33-33-33-3-1-113-31-1-1-1-11111-33-33-11−i−iii−i−iii0000−iii−i1-1−iii−ii−i1-1i−iii−i−iii−i−i000000−ii−ii0000
χ4133-3-33-3-333-33-3-1-11-331-1-111-1-1113-3-331-1ii−i−iii−i−i0000−iii−i-11−iii−i−ii1-1−ii−i−iiiii−i−i000000−iii−i0000
χ4233-3-33-3-333-33-3-1-11-331-1-111-1-1113-3-331-1−i−iii−i−iii0000i−i−ii-11i−i−iii−i1-1i−iii−i−i−i−iii000000i−i−ii0000
χ4333-3-33-3-333-33-3-1-11-331-1-111-1-111-333-31-1ii−i−iii−i−i0000−ii−ii1-1−ii−iii−i-11i−i−i−iiiii−i−i000000i−i−ii0000
χ4433-3-33-3-333-33-3-1-11-331-1-111-1-111-333-31-1−i−iii−i−iii0000i−ii−i1-1i−ii−i−ii-11−iiii−i−i−i−iii000000−iii−i0000
χ454444-4-40044-4-44-4-40044-40000-4400000000000000-2-2-2-200000000000000000000000022000000000000
χ4644-4-4-44004-4-444-4400-44-400004-400000000000000-222-2000000000000000000000000-22000000000000
χ4766666666-2-2-2-22-2-2-2-22-22-2-2-2-22-200002200000000000000220000-2-22200-2-20000000000000000000000
χ4866666666-2-2-2-22-2-2-2-22-22-2-2-2-22-200002200000000000000-2-2000022-2-200220000000000000000000000
χ4966666666-2-2-2-2-222-2-2-22-22222-220000-2-22222-2-2-2-20000220000-2-2000000000000000000000000000000
χ5066666666-2-2-2-2-222-2-2-22-22222-220000-2-2-2-2-2-222220000-2-2000022000000000000000000000000000000
χ51666666-6-6-2-2-2-22-2-2222-2222222-20000-2-200000000000000220000-2-2-2-200220000000000000000000000
χ52666666-6-6-2-2-2-22-2-2222-2222222-20000-2-200000000000000-2-20000222200-2-20000000000000000000000
χ53666666-6-6-2-2-2-2-22222-22-2-2-2-2-2-220000222222-2-2-2-20000-2-2000022000000000000000000000000000000
χ54666666-6-6-2-2-2-2-22222-22-2-2-2-2-2-22000022-2-2-2-222220000220000-2-2000000000000000000000000000000
χ556666-6-60066-6-6-22200-2-2200002-20000002-22-22-22-200000000000000000000-22-22000000000000000000
χ566666-6-60066-6-6-22200-2-2200002-2000000-22-22-22-22000000000000000000002-22-2000000000000000000
χ576666-6-600-2-222-2-2-200-2224-44-4220000002-22-2-22-220000000000000000000000002-22-200000000000000
χ586666-6-600-2-222-2-2-200-2224-44-422000000-22-222-22-2000000000000000000000000-22-2200000000000000
χ596666-6-600-2-222-2-2-200-222-44-44220000002-22-2-22-22000000000000000000000000-22-2200000000000000
χ606666-6-600-2-222-2-2-200-222-44-4422000000-22-222-22-20000000000000000000000002-22-200000000000000
χ6166-6-66-66-6-22-222-22-22-2-22-2-222-2200002-2000000000000002i−2i0000−2i2i2i−2i00−2i2i0000000000000000000000
χ6266-6-66-66-6-22-222-22-22-2-22-2-222-2200002-200000000000000−2i2i00002i−2i−2i2i002i−2i0000000000000000000000
χ6366-6-66-66-6-22-22-22-2-2222-222-2-22-20000-222i2i−2i−2i−2i−2i2i2i00002i−2i0000−2i2i000000000000000000000000000000
χ6466-6-66-66-6-22-22-22-2-2222-222-2-22-20000-22−2i−2i2i2i2i2i−2i−2i0000−2i2i00002i−2i000000000000000000000000000000
χ6566-6-66-6-66-22-222-222-2-2-2222-2-2-220000-22000000000000002i−2i0000−2i2i−2i2i002i−2i0000000000000000000000
χ6666-6-66-6-66-22-222-222-2-2-2222-2-2-220000-2200000000000000−2i2i00002i−2i2i−2i00−2i2i0000000000000000000000
χ6766-6-66-6-66-22-22-22-22-222-2-2-2222-200002-22i2i−2i−2i−2i−2i2i2i0000−2i2i00002i−2i000000000000000000000000000000
χ6866-6-66-6-66-22-22-22-22-222-2-2-2222-200002-2−2i−2i2i2i2i2i−2i−2i00002i−2i0000−2i2i000000000000000000000000000000
χ6966-6-6-66006-6-66-22-2002-220000-220000002i−2i−2i2i2i−2i−2i2i00000000000000000000−2i2i2i−2i000000000000000000
χ7066-6-6-66006-6-66-22-2002-220000-22000000−2i2i2i−2i−2i2i2i−2i000000000000000000002i−2i−2i2i000000000000000000
χ7166-6-6-6600-222-2-2-22002224-4-44-2-20000002i−2i−2i2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i00000000000000
χ7266-6-6-6600-222-2-2-22002224-4-44-2-2000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i00000000000000
χ7366-6-6-6600-222-2-2-2200222-444-4-2-20000002i−2i−2i2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i00000000000000
χ7466-6-6-6600-222-2-2-2200222-444-4-2-2000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i00000000000000
χ7512121212-12-1200-4-444444004-4-40000-4-400000000000000000000000000000000000000000000000000000000
χ761212-12-12-121200-444-444-400-4-4-400004400000000000000000000000000000000000000000000000000000000
χ7716-1616-1600000000000000000000000000000000000044-4-400000000000000000000000000000000000000
χ7816-1616-16000000000000000000000000000000000000-2-22200000000000000000000000000i6−i6i6−i600000000
χ7916-1616-16000000000000000000000000000000000000-2-22200000000000000000000000000−i6i6−i6i600000000
χ8016-16-16160000000000000000000000000000000000004-44-400000000000000000000000000000000000000
χ8116-16-1616000000000000000000000000000000000000-22-2200000000000000000000000000i6−i6−i6i600000000
χ8216-16-1616000000000000000000000000000000000000-22-2200000000000000000000000000−i6i6i6−i600000000

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