Finite Group Databasebeta

← Group #72219506

Character table — Group #72219506

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122244444444888888888881616161616161616161616163232323232323232323232323232323232323232323264646464646464646464646464646464
order12222222244442224444444422222444444422444444444444888888884444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-11-11-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ711111111111111111111111111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1
χ91111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1ii−i−i1111-1-1-1-1i−iii−i−i11-1-111-1-11-1ii−i−i1-1ii−i−iii−i−i
χ101111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1ii−i−i1-11-1-1-111i−iii−i−i-1-111-1-111-11ii−i−i1-1−i−iii−i−iii
χ111111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1ii−i−i-11-1111-1-1i−iii−i−i-1-11111-1-1-11−i−iii-11ii−i−i−i−iii
χ121111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1ii−i−i-1-1-1-11111i−iii−i−i11-1-1-1-1111-1−i−iii-11−i−iiiii−i−i
χ131111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1−i−iii1111-1-1-1-1−ii−i−iii11-1-111-1-11-1−i−iii1-1−i−iii−i−iii
χ141111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1−i−iii1-11-1-1-111−ii−i−iii-1-111-1-111-11−i−iii1-1ii−i−iii−i−i
χ151111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1−i−iii-11-1111-1-1−ii−i−iii-1-11111-1-1-11ii−i−i-11−i−iiiii−i−i
χ161111111-1-1111111-1-1-111-1-1-1-111-1-1-111-1−i−iii-1-1-1-11111−ii−i−iii11-1-1-1-1111-1ii−i−i-11ii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-22-22-22-2-2-200002020220000000000000000000000-2-200000000
χ18222222222222222222-2-2-2-2-2-22-22-22-2-2-20000-20-20-2-200000000000000000000002200000000
χ192222222222222-2-222222-2-222-2-2-2-2-2-2220000020200220000000000-2-2-2-20000000000000000
χ202222222222222-2-222222-2-222-2-2-2-2-2-22200000-20-200-2-2000000000022220000000000000000
χ212222222222222-2-2222-2-222-2-2-22-22-22-2-200000000000000000022220000-2-200000000000000
χ222222222222222-2-2222-2-222-2-2-22-22-22-2-2000000000000000000-2-2-2-200002200000000000000
χ232222222-2-2222222-2-2-2-2-222222-2-22-2-2-2200002020-2-20000000000000000000000-2200000000
χ242222222-2-2222222-2-2-2-2-222222-2-22-2-2-220000-20-202200000000000000000000002-200000000
χ252222222-2-22222-2-2-2-2-22222-2-2-2-2222-22-20000020200-2-20000000000-2-2220000000000000000
χ262222222-2-22222-2-2-2-2-22222-2-2-2-2222-22-200000-20-20022000000000022-2-20000000000000000
χ272222222-2-22222-2-2-2-2-2-2-2-2-222-222-222-2200000000000000000022-2-20000-2200000000000000
χ282222222-2-22222-2-2-2-2-2-2-2-2-222-222-222-22000000000000000000-2-22200002-200000000000000
χ2922222-2-222-22-2222-22-2222222-2-22-2-22-2-200000000000000000000000000000000002-22-20000
χ3022222-2-222-22-2222-22-2222222-2-22-2-22-2-20000000000000000000000000000000000-22-220000
χ3122222-2-222-22-2222-22-2-2-2-2-2-2-2-2222-2-222000000000000000000000000000000000000002i−2i2i−2i
χ3222222-2-222-22-2222-22-2-2-2-2-2-2-2-2222-2-22200000000000000000000000000000000000000−2i2i−2i2i
χ3322222-2-222-22-22-2-2-22-222-2-22222-222-2-2-2222200000000-2-22-22-2000000000000000000000000
χ3422222-2-222-22-22-2-2-22-222-2-22222-222-2-2-2-2-2-2-20000000022-22-22000000000000000000000000
χ3522222-2-222-22-22-2-2-22-2-2-222-2-22-2-2-2222200000000000000000000000000002-22-20000000000
χ3622222-2-222-22-22-2-2-22-2-2-222-2-22-2-2-222220000000000000000000000000000-22-220000000000
χ3722222-2-2-2-2-22-22222-2222-2-2-2-2-2-2-2222-2200000000000000000000000000000000002i−2i−2i2i0000
χ3822222-2-2-2-2-22-22222-2222-2-2-2-2-2-2-2222-220000000000000000000000000000000000−2i2i2i−2i0000
χ3922222-2-2-2-2-22-22222-22-2-22222-22-2-22-22-2000000000000000000000000000000000000002-2-22
χ4022222-2-2-2-2-22-22222-22-2-22222-22-2-22-22-200000000000000000000000000000000000000-222-2
χ4122222-2-2-2-2-22-22-2-22-222222-2-2222-2-2-2-222i2i−2i−2i00000000−2i2i2i−2i−2i2i000000000000000000000000
χ4222222-2-2-2-2-22-22-2-22-222222-2-2222-2-2-2-22−2i−2i2i2i000000002i−2i−2i2i2i−2i000000000000000000000000
χ4322222-2-2-2-2-22-22-2-22-22-2-2-2-2222-222-222-200000000000000000000000000002i−2i−2i2i0000000000
χ4422222-2-2-2-2-22-22-2-22-22-2-2-2-2222-222-222-20000000000000000000000000000−2i2i2i−2i0000000000
χ45444444444-4-4-4-4004-4-400000000000000222200000000-2-2-22-22000000000000000000000000
χ46444444444-4-4-4-4004-4-400000000000000-2-2-2-200000000222-22-2000000000000000000000000
χ474444444-4-4-4-4-4-400-444000000000000002i2i−2i−2i00000000−2i2i−2i2i2i−2i000000000000000000000000
χ484444444-4-4-4-4-4-400-44400000000000000−2i−2i2i2i000000002i−2i2i−2i−2i2i000000000000000000000000
χ4944444-4-4444-44-400-4-440000000000000022220000000022-2-2-2-2000000000000000000000000
χ5044444-4-4444-44-400-4-4400000000000000-2-2-2-200000000-2-22222000000000000000000000000
χ5144444-4-4-4-44-44-40044-4000000000000002i2i−2i−2i000000002i−2i−2i−2i2i2i000000000000000000000000
χ5244444-4-4-4-44-44-40044-400000000000000−2i−2i2i2i00000000−2i2i2i2i−2i−2i000000000000000000000000
χ5344-4-4400000-4044-4000004-44-4000000000000020-2002-200000000002-22-20000000000000000
χ5444-4-4400000-4044-4000004-44-40000000000000-20200-220000000000-22-220000000000000000
χ5544-4-4400000-4044-400000-44-44000000000000020-200-2200000000002-2-220000000000000000
χ5644-4-4400000-4044-400000-44-440000000000000-202002-20000000000-222-20000000000000000
χ5744-4-4400000-404-44000004-4-44000000000000020-200-220000000000-222-20000000000000000
χ5844-4-4400000-404-44000004-4-440000000000000-202002-200000000002-2-220000000000000000
χ5944-4-4400000-404-4400000-444-4000000000000020-2002-20000000000-22-220000000000000000
χ6044-4-4400000-404-4400000-444-40000000000000-20200-2200000000002-22-20000000000000000
χ61888-8-8000080-800000000000000000000000000000000000000004i−4i00000000000000000000
χ62888-8-8000080-80000000000000000000000000000000000000000−4i4i00000000000000000000
χ63888-8-80000-808000000000000000000000000000000000000004-40000000000000000000000
χ64888-8-80000-80800000000000000000000000000000000000000-440000000000000000000000
χ6588-88-88-80000000000000000000000000000000004-400000000000000000000000000000000
χ6688-88-88-8000000000000000000000000000000000-4400000000000000000000000000000000
χ6788-88-8-880000000000000000000000000000040-400000000000000000000000000000000000
χ6888-88-8-8800000000000000000000000000000-40400000000000000000000000000000000000
χ6988-8-880000080-8000008-8000000000000000000000000000000000000000000000000000000
χ7088-8-880000080-800000-88000000000000000000000000000000000000000000000000000000
χ7116-16000008-8000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ7216-16000008-800000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ7316-1600000-88000000000000000000000004-4-4400000000000000000000000000000000000000
χ7416-1600000-8800000000000000000000000-444-400000000000000000000000000000000000000

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