Finite Group Databasebeta

← Group #72317545

Character table — Group #72317545

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222224444444444448888888816161616161616161616161616161616161616161616161632323232323232323232323232323232
order1244222444222222444444222244444444444488888888888888888888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111111-1-1-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−i111111-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−i1111-1-111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iii
χ11111111111111-1-1-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-111-1-1111111-1-1-1-111−i−iii−i−iiiii−i−i
χ12111111111111-1-1-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−i−i−iii
χ13111111111111-1-1-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii111111-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii
χ14111111111111-1-1-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii1111-1-111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i
χ15111111111111-1-1-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-111-1-1111111-1-1-1-111ii−i−iii−i−i−i−iii
χ16111111111111-1-1-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iiiii−i−i
χ1722222222222222-2-2-2-22222-2-22-2-2-22-200000000000022220000-2-2-2-20000000000000000
χ1822222222222222-2-2-2-22222-2-22-2-2-22-2000000000000-2-2-2-2000022220000000000000000
χ19222222222222-2-2222222-2-2-2-2-22-2-2-2200000000000022-2-20000-2-2220000000000000000
χ20222222222222-2-2222222-2-2-2-2-22-2-2-22000000000000-2-222000022-2-20000000000000000
χ212222222222-2-2222222-2-2222-2-2-22-2-2-200000000000000000000000000002-22-200000000
χ222222222222-2-2222222-2-2222-2-2-22-2-2-20000000000000000000000000000-22-2200000000
χ232222222222-2-222-2-2-2-2-2-222-22-22-22-22000000000000000000000000000000002-22-20000
χ242222222222-2-222-2-2-2-2-2-222-22-22-22-2200000000000000000000000000000000-22-220000
χ252222222222-2-2-2-22222-2-2-2-2-222-2-222-2000000000000000000000000000000002i−2i−2i2i0000
χ262222222222-2-2-2-22222-2-2-2-2-222-2-222-200000000000000000000000000000000−2i2i2i−2i0000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-22-2222-22200000000000000000000000000002i−2i−2i2i00000000
χ282222222222-2-2-2-2-2-2-2-2-2-2-2-22-2222-2220000000000000000000000000000−2i2i2i−2i00000000
χ2922-2-2222-2-2-2222222-2-2-2-2-2-22-2-22-222-222-2-222-2-200000000000000000000000000000000
χ3022-2-2222-2-2-2222222-2-2-2-2-2-22-2-22-222-2-2-222-2-22200000000000000000000000000000000
χ3122-2-2222-2-2-22222-2-222-2-2-2-2-22-2-22-2220000000000000000000000000000000000002-22-2
χ3222-2-2222-2-2-22222-2-222-2-2-2-2-22-2-22-222000000000000000000000000000000000000-22-22
χ3322-2-2222-2-2-222-2-222-2-2-2-222-22222-2-2-20000000000000000000000000000000000002i−2i−2i2i
χ3422-2-2222-2-2-222-2-222-2-2-2-222-22222-2-2-2000000000000000000000000000000000000−2i2i2i−2i
χ3522-2-2222-2-2-222-2-2-2-222-2-2222-22-2-22-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3622-2-2222-2-2-222-2-2-2-222-2-2222-22-2-22-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3722-2-2222-2-2-2-2-22222-2-222-2-2222-2-2-2-22000000002i2i−2i−2i00002i2i−2i−2i00000000000000000000
χ3822-2-2222-2-2-2-2-22222-2-222-2-2222-2-2-2-2200000000−2i−2i2i2i0000−2i−2i2i2i00000000000000000000
χ3922-2-2222-2-2-2-2-222-2-22222-2-2-2-22222-2-20000000000000000000000002-22-2000000000000
χ4022-2-2222-2-2-2-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000-22-22000000000000
χ4122-2-2222-2-2-2-2-2-2-222-2-22222-2-2-2-222220000000000000000000000002-2-22000000000000
χ4222-2-2222-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000-222-2000000000000
χ4322-2-2222-2-2-2-2-2-2-2-2-222222222-22-2-22-2000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ4422-2-2222-2-2-2-2-2-2-2-2-222222222-22-2-22-200000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ4544444-4-4-44-4004-40000004-400000000000000002-22-200002-22-200000000000000000000
χ4644444-4-4-44-4004-40000004-40000000000000000-22-220000-22-2200000000000000000000
χ4744444-4-4-44-400-44000000-4400000000000000002-22-20000-22-2200000000000000000000
χ4844444-4-4-44-400-44000000-440000000000000000-22-2200002-22-200000000000000000000
χ494444-44-4-4-444-40000004-4000000000000000000000000000000004-40000000000000000
χ504444-44-4-4-444-40000004-400000000000000000000000000000000-440000000000000000
χ514444-44-4-4-44-44000000-440000000000000000000000000000004-4000000000000000000
χ524444-44-4-4-44-44000000-44000000000000000000000000000000-44000000000000000000
χ5344-4-44-4-44-44004-4000000-4400000000000000002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ5444-4-44-4-44-44004-4000000-440000000000000000−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ5544-4-44-4-44-4400-440000004-400000000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ5644-4-44-4-44-4400-440000004-40000000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ5744-4-4-44-444-44-4000000-4400000000000000000000004i−4i00000000000000000000000000
χ5844-4-4-44-444-44-4000000-440000000000000000000000−4i4i00000000000000000000000000
χ5944-4-4-44-444-4-440000004-40000000000000000000000004i−4i000000000000000000000000
χ6044-4-4-44-444-4-440000004-4000000000000000000000000−4i4i000000000000000000000000
χ618888-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ6288-8-8-8-88-888000000000000000000000000000000000000000000000000000000000000
χ638-88i−8i00000000004-44i−4i0000000000002-22i−2i2-22i−2i00000000000000000000000000000000
χ648-88i−8i00000000004-44i−4i000000000000-22−2i2i-22−2i2i00000000000000000000000000000000
χ658-88i−8i0000000000-44−4i4i0000000000002i−2i-22−2i2i2-200000000000000000000000000000000
χ668-88i−8i0000000000-44−4i4i000000000000−2i2i2-22i−2i-2200000000000000000000000000000000
χ678-8−8i8i00000000004-4−4i4i0000000000002-2−2i2i2-2−2i2i00000000000000000000000000000000
χ688-8−8i8i00000000004-4−4i4i000000000000-222i−2i-222i−2i00000000000000000000000000000000
χ698-8−8i8i0000000000-444i−4i0000000000002i−2i2-2−2i2i-2200000000000000000000000000000000
χ708-8−8i8i0000000000-444i−4i000000000000−2i2i-222i−2i2-200000000000000000000000000000000

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