Finite Group Databasebeta

← Group #72341862

Character table — Group #72341862

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111224466668888121212121212121212121616242424242424242432323232323232324848484848484848484848484848484848486464646464646464646464649696969696969696
order1222444422444444222244444422444444443666121212122244444444888888886666121212121212121244448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-1111111-1-111-1-1
χ4111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-11111-1-111-1-111
χ5111111-1-111111111111111-1-111-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ6111111-1-111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ7111111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ8111111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ911-1-11-1i−i1-11-1i−ii−i-1-11111i−i-1-11-1i−ii−iii−i−i11-1-1ii−i−i1-1i−i1-11-1i−ii−i1-1i−i1-111-1-11-1i−iii−i−i1-11-1i−ii−i
χ1011-1-11-1i−i1-11-1i−ii−i-1-11111i−i-1-11-1i−ii−iii−i−i11-1-1ii−i−i-11−ii1-1-11−ii−ii-11−ii-1111-1-11-1i−iii−i−i-11-11−ii−ii
χ1111-1-11-1i−i1-11-1−ii−ii-1-11111i−i-1-1-11i−ii−i−i−iii11-1-1−i−iii1-1−ii-111-1−iii−i-11i−i-11-1-1111-1−iiii−i−i1-1-11i−i−ii
χ1211-1-11-1i−i1-11-1−ii−ii-1-11111i−i-1-1-11i−ii−i−i−iii11-1-1−i−iii-11i−i-11-11i−i−ii1-1−ii1-1-1-1111-1−iiii−i−i-111-1−iii−i
χ1311-1-11-1−ii1-11-1i−ii−i-1-11111−ii-1-1-11−ii−iiii−i−i11-1-1ii−i−i1-1i−i-111-1i−i−ii-11−ii-11-1-1111-1i−i−i−iii1-1-11−iii−i
χ1411-1-11-1−ii1-11-1i−ii−i-1-11111−ii-1-1-11−ii−iiii−i−i11-1-1ii−i−i-11−ii-11-11−iii−i1-1i−i1-1-1-1111-1i−i−i−iii-111-1i−i−ii
χ1511-1-11-1−ii1-11-1−ii−ii-1-11111−ii-1-11-1−ii−ii−i−iii11-1-1−i−iii1-1−ii1-11-1−ii−ii1-1−ii1-111-1-11-1−ii−i−iii1-11-1−ii−ii
χ1611-1-11-1−ii1-11-1−ii−ii-1-11111−ii-1-11-1−ii−ii−i−iii11-1-1−i−iii-11i−i1-1-11i−ii−i-11i−i-1111-1-11-1−ii−i−iii-11-11i−ii−i
χ17222222222222222222222222222222222222-1-1-1-1-1-1-1-1000022000000000000-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222222222222-2-2-2-22222222222-2-22222-2-2-2-2-1-1-1-111110000-2-20000000000001111-1-111-1-1-1-100000000
χ19222222-2-222222222222222-2-222-2-2-2-2-2-22222-1-1-1-1-1-1-1-10000-2-20000000000001111-1-1-1-1111100000000
χ20222222-2-22222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-1-1-1-11111000022000000000000-1-1-1-1-1-111111100000000
χ212222-2-20022-2-222-2-22-22-22-2002-20000002-22-2222222220000000000000000000000-2-2-2-2000000000000
χ222222-2-20022-2-222-2-22-22-22-2002-20000002-22-2-1-1-1-1-1-1-1-1000000000000000000−i3i3−i3i31111−i3i3−i3i300000000
χ232222-2-20022-2-222-2-22-22-22-2002-20000002-22-2-1-1-1-1-1-1-1-1000000000000000000i3−i3i3−i31111i3−i3i3−i300000000
χ242222-2-20022-2-2-2-2222-22-22-2002-2000000-22-222222-2-2-2-20000000000000000000000-2-222000000000000
χ252222-2-20022-2-2-2-2222-22-22-2002-2000000-22-22-1-1-1-11111000000000000000000−i3i3−i3i311-1-1i3−i3i3−i300000000
χ262222-2-20022-2-2-2-2222-22-22-2002-2000000-22-22-1-1-1-11111000000000000000000i3−i3i3−i311-1-1−i3i3−i3i300000000
χ2722-2-22-22i−2i2-22-22i−2i2i−2i-2-222222i−2i-2-22-22i−2i2i−2i2i2i−2i−2i-1-111−i−iii00002-2000000000000-1-111-11−ii−i−iii00000000
χ2822-2-22-22i−2i2-22-2−2i2i−2i2i-2-222222i−2i-2-2-222i−2i2i−2i−2i−2i2i2i-1-111ii−i−i0000-2200000000000011-1-1-11i−i−i−iii00000000
χ2922-2-22-2−2i2i2-22-22i−2i2i−2i-2-22222−2i2i-2-2-22−2i2i−2i2i2i2i−2i−2i-1-111−i−iii0000-2200000000000011-1-1-11−iiii−i−i00000000
χ3022-2-22-2−2i2i2-22-2−2i2i−2i2i-2-22222−2i2i-2-22-2−2i2i−2i2i−2i−2i2i2i-1-111ii−i−i00002-2000000000000-1-111-11i−iii−i−i00000000
χ3122-2-2-22002-2-222i−2i−2i2i-222-22-200-220000002i−2i−2i2i22-2-22i2i−2i−2i0000000000000000000000-22−2i2i000000000000
χ3222-2-2-22002-2-222i−2i−2i2i-222-22-200-220000002i−2i−2i2i-1-111−i−iii000000000000000000−i3i3i3−i31-1i−i3−3−3300000000
χ3322-2-2-22002-2-222i−2i−2i2i-222-22-200-220000002i−2i−2i2i-1-111−i−iii000000000000000000i3−i3−i3i31-1i−i−333−300000000
χ3422-2-2-22002-2-22−2i2i2i−2i-222-22-200-22000000−2i2i2i−2i22-2-2−2i−2i2i2i0000000000000000000000-222i−2i000000000000
χ3522-2-2-22002-2-22−2i2i2i−2i-222-22-200-22000000−2i2i2i−2i-1-111ii−i−i000000000000000000−i3i3i3−i31-1−ii−333−300000000
χ3622-2-2-22002-2-22−2i2i2i−2i-222-22-200-22000000−2i2i2i−2i-1-111ii−i−i000000000000000000i3−i3−i3i31-1−ii3−3−3300000000
χ373333333333333333-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-1000000001111-1-1111111111111000000000000-1-1-1-1-1-1-1-1
χ383333333333333333-1-1-1-1-1-133-1-133-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000011111111
χ39333333333333-3-3-3-3-1-1-1-1-1-133-1-1-3-3-1-1-1-111110000000011-1-11111-1-111-1-111-1-1000000000000-1-111-1-111
χ40333333333333-3-3-3-3-1-1-1-1-1-133-1-1-3-3-1-1-1-1111100000000-1-11111-1-111-1-111-1-11100000000000011-1-111-1-1
χ41333333-3-333333333-1-1-1-1-1-1-3-3-1-1-3-31111-1-1-1-1000000001111111111-1-1-1-1-1-1-1-1000000000000-1-11111-1-1
χ42333333-3-333333333-1-1-1-1-1-1-3-3-1-1-3-31111-1-1-1-100000000-1-1-1-111-1-1-1-11111111100000000000011-1-1-1-111
χ43333333-3-33333-3-3-3-3-1-1-1-1-1-1-3-3-1-133111111110000000011-1-1-1-111-1-1-1-111-1-111000000000000-1-1-1-11111
χ44333333-3-33333-3-3-3-3-1-1-1-1-1-1-3-3-1-1331111111100000000-1-111-1-1-1-11111-1-111-1-10000000000001111-1-1-1-1
χ4533-3-33-33i−3i3-33-33i−3i3i−3i11-1-1-1-13i−3i113-3−ii−ii−i−iii000000001-1i−i-111-1i−ii−i1-1i−i1-1000000000000-11-11−ii−ii
χ4633-3-33-33i−3i3-33-33i−3i3i−3i11-1-1-1-13i−3i113-3−ii−ii−i−iii00000000-11−ii-11-11−ii−ii-11−ii-110000000000001-11-1i−ii−i
χ4733-3-33-33i−3i3-33-3−3i3i−3i3i11-1-1-1-13i−3i11-33−ii−iiii−i−i000000001-1−ii1-11-1−iii−i-11i−i-11000000000000-111-1−iii−i
χ4833-3-33-33i−3i3-33-3−3i3i−3i3i11-1-1-1-13i−3i11-33−ii−iiii−i−i00000000-11i−i1-1-11i−i−ii1-1−ii1-10000000000001-1-11i−i−ii
χ4933-3-33-3−3i3i3-33-33i−3i3i−3i11-1-1-1-1−3i3i11-33i−ii−i−i−iii000000001-1i−i1-11-1i−i−ii-11−ii-11000000000000-111-1i−i−ii
χ5033-3-33-3−3i3i3-33-33i−3i3i−3i11-1-1-1-1−3i3i11-33i−ii−i−i−iii00000000-11−ii1-1-11−iii−i1-1i−i1-10000000000001-1-11−iii−i
χ5133-3-33-3−3i3i3-33-3−3i3i−3i3i11-1-1-1-1−3i3i113-3i−ii−iii−i−i000000001-1−ii-111-1−ii−ii1-1−ii1-1000000000000-11-11i−ii−i
χ5233-3-33-3−3i3i3-33-3−3i3i−3i3i11-1-1-1-1−3i3i113-3i−ii−iii−i−i00000000-11i−i-11-11i−ii−i-11i−i-110000000000001-11-1−ii−ii
χ5366666666-2-2-2-200002-22-2-22-2-2-220022-2-2000000000000220000-2-2002200-2-20000000000000000000000
χ5466666666-2-2-2-200002-22-2-22-2-2-220022-2-2000000000000-2-200002200-2-200220000000000000000000000
χ5566666666-2-2-2-20000-22-222-2-2-22-200-2-22200000000000000220000-2-2002200-2-200000000000000000000
χ5666666666-2-2-2-20000-22-222-2-2-22-200-2-22200000000000000-2-200002200-2-2002200000000000000000000
χ57666666-6-6-2-2-2-200002-22-2-2222-2200-2-222000000000000220000-2-200-2-200220000000000000000000000
χ58666666-6-6-2-2-2-200002-22-2-2222-2200-2-222000000000000-2-2000022002200-2-20000000000000000000000
χ59666666-6-6-2-2-2-20000-22-222-2222-20022-2-200000000000000220000-2-200-2-2002200000000000000000000
χ60666666-6-6-2-2-2-20000-22-222-2222-20022-2-200000000000000-2-2000022002200-2-200000000000000000000
χ616666-6-60066-6-666-6-6-22-22-2200-22000000-22-220000000000000000000000000000000000000000000000
χ626666-6-60066-6-6-6-666-22-22-2200-220000002-22-20000000000000000000000000000000000000000000000
χ6366-6-66-66i−6i-22-2200002-2-222-2−2i2i-2200−2i2i2i−2i000000000000002i−2i0000−2i2i002-200-2200000000000000000000
χ6466-6-66-66i−6i-22-2200002-2-222-2−2i2i-2200−2i2i2i−2i00000000000000−2i2i00002i−2i00-22002-200000000000000000000
χ6566-6-66-66i−6i-22-220000-222-2-22−2i2i2-2002i−2i−2i2i0000000000002-20000-22002i−2i00−2i2i0000000000000000000000
χ6666-6-66-66i−6i-22-220000-222-2-22−2i2i2-2002i−2i−2i2i000000000000-2200002-200−2i2i002i−2i0000000000000000000000
χ6766-6-66-6−6i6i-22-2200002-2-222-22i−2i-22002i−2i−2i2i000000000000002i−2i0000−2i2i00-22002-200000000000000000000
χ6866-6-66-6−6i6i-22-2200002-2-222-22i−2i-22002i−2i−2i2i00000000000000−2i2i00002i−2i002-200-2200000000000000000000
χ6966-6-66-6−6i6i-22-220000-222-2-222i−2i2-200−2i2i2i−2i0000000000002-20000-2200−2i2i002i−2i0000000000000000000000
χ7066-6-66-6−6i6i-22-220000-222-2-222i−2i2-200−2i2i2i−2i000000000000-2200002-2002i−2i00−2i2i0000000000000000000000
χ7166-6-6-66006-6-666i−6i−6i6i2-2-22-22002-2000000−2i2i2i−2i0000000000000000000000000000000000000000000000
χ7266-6-6-66006-6-66−6i6i6i−6i2-2-22-22002-20000002i−2i−2i2i0000000000000000000000000000000000000000000000
χ7312121212-12-1200-4-44400004444-4-400-4-400000000000000000000000000000000000000000000000000000000
χ7412121212-12-1200-4-4440000-4-4-4-444004400000000000000000000000000000000000000000000000000000000
χ751212-12-12-121200-444-4000044-4-44400-4-400000000000000000000000000000000000000000000000000000000
χ761212-12-12-121200-444-40000-4-444-4-4004400000000000000000000000000000000000000000000000000000000
χ7716-1616-16000000000000000000000000000000004-4-44000000000000000000000000000000000000000000
χ7816-1616-1600000000000000000000000000000000-222-2−2i32i3−2i32i300000000000000000000000000000000000000
χ7916-1616-1600000000000000000000000000000000-222-22i3−2i32i3−2i300000000000000000000000000000000000000
χ8016-16-1616000000000000000000000000000000004-44-4000000000000000000000000000000000000000000
χ8116-16-161600000000000000000000000000000000-22-2223−23−232300000000000000000000000000000000000000
χ8216-16-161600000000000000000000000000000000-22-22−232323−2300000000000000000000000000000000000000

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