Finite Group Databasebeta

← Group #72258417

Character table — Group #72258417

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size111122222244444444444488888888888888881616161616161616161616163232323232323232323232323232323232323232
order1244222444222222444444222222224444444444448888888844444444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111-1-111-1-1111-1-11111-11-1-11111-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i
χ1011111111111111-1-111-1-1111-1-11111-11-1-11111-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii11-1-1−i−iii
χ1111111111111111-1-111-1-1111-1-11111-11-1-11111-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i-1-111−i−iii
χ1211111111111111-1-111-1-1111-1-11111-11-1-11111-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iii-1-111ii−i−i
χ1311111111111111-1-111-1-1111-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1ii−i−iii−i−i−i−iii-1-111−i−iii
χ1411111111111111-1-111-1-1111-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-111-1-1−i−iii−i−iiiii−i−i-1-111ii−i−i
χ1511111111111111-1-111-1-1111-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-111-1-111ii−i−i−i−iii−i−iii11-1-1ii−i−i
χ1611111111111111-1-111-1-1111-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-111-1-111−i−iiiii−i−iii−i−i11-1-1−i−iii
χ17222222222222-2-2222222-2-2-2-2-200002-22-20000-20000000000002-22-20000000000000000
χ18222222222222-2-2222222-2-2-2-2-200002-22-20000-2000000000000-22-220000000000000000
χ19222222222222-2-2-2-222-2-2-2-2-2220000-2-2-22000020000000000002i−2i−2i2i0000000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2220000-2-2-2200002000000000000−2i2i2i−2i0000000000000000
χ212222222222-2-22222-2-22222-22-20000-2-2-220000-200002222-2-2-2-200000000000000000000
χ222222222222-2-22222-2-22222-22-20000-2-2-220000-20000-2-2-2-2222200000000000000000000
χ232222222222-2-222-2-2-2-2-2-222-2-2200002-22-200002000022-2-2-2-22200000000000000000000
χ242222222222-2-222-2-2-2-2-2-222-2-2200002-22-2000020000-2-22222-2-200000000000000000000
χ252222222222-2-2-2-222-2-222-2-22-220000-22-2-20000200000000000000002-22-2000000000000
χ262222222222-2-2-2-222-2-222-2-22-220000-22-2-2000020000000000000000-22-22000000000000
χ272222222222-2-2-2-2-2-2-2-2-2-2-2-222-2000022220000-200000000000000002i−2i−2i2i000000000000
χ282222222222-2-2-2-2-2-2-2-2-2-2-2-222-2000022220000-20000000000000000−2i2i2i−2i000000000000
χ2922-2-2222-2-2-2222222-2-2-2-2-2-22-2-222222-2-22-2-2-2-2222-2-20000000000000000000000000000
χ3022-2-2222-2-2-2222222-2-2-2-2-2-22-2-2-2-2-2-22-2-2222222-2-2220000000000000000000000000000
χ3122-2-2222-2-2-22222-2-2-2-222-2-22222222-2-22-2-2-2-2-2-2-2-2220000000000000000000000000000
χ3222-2-2222-2-2-22222-2-2-2-222-2-2222-2-2-2-2-2-22-22222-222-2-20000000000000000000000000000
χ3322-2-2222-2-2-222-2-222-2-2-2-222-222000022-2-20000-2000000000000000000002-22-200000000
χ3422-2-2222-2-2-222-2-222-2-2-2-222-222000022-2-20000-200000000000000000000-22-2200000000
χ3522-2-2222-2-2-222-2-2-2-2-2-22222-2-2-20000-222200002000000000000000000002i−2i−2i2i00000000
χ3622-2-2222-2-2-222-2-2-2-2-2-22222-2-2-20000-22220000200000000000000000000−2i2i2i−2i00000000
χ3722-2-2222-2-2-2-2-2222222-2-2-2-2-2-220000-22220000-20000000000000000000000002i−2i2i−2i0000
χ3822-2-2222-2-2-2-2-2222222-2-2-2-2-2-220000-22220000-2000000000000000000000000−2i2i−2i2i0000
χ3922-2-2222-2-2-2-2-222-2-22222-2-2-22-2000022-2-2000020000000000000000000000002i−2i−2i2i0000
χ4022-2-2222-2-2-2-2-222-2-22222-2-2-22-2000022-2-200002000000000000000000000000−2i2i2i−2i0000
χ4122-2-2222-2-2-2-2-2-2-22222-2-22222-20000-2-22-20000200000000000000000000000000002-22-2
χ4222-2-2222-2-2-2-2-2-2-22222-2-22222-20000-2-22-2000020000000000000000000000000000-22-22
χ4322-2-2222-2-2-2-2-2-2-2-2-22222222-2200002-2-220000-200000000000000000000000000002i−2i−2i2i
χ4422-2-2222-2-2-2-2-2-2-2-2-22222222-2200002-2-220000-20000000000000000000000000000−2i2i2i−2i
χ4544444-4-4-4-44004-40000004-4000000000000000000000000004-400000000000000000000
χ4644444-4-4-4-44004-40000004-400000000000000000000000000-4400000000000000000000
χ4744444-4-4-4-4400-44000000-440000000000000000000000004-40000000000000000000000
χ4844444-4-4-4-4400-44000000-44000000000000000000000000-440000000000000000000000
χ494444-4-444-4-400004-4004-40000022-2-2000022-2-202-22-20000000000000000000000000000
χ504444-4-444-4-400004-4004-400000-2-2220000-2-2220-22-220000000000000000000000000000
χ514444-4-444-4-40000-4400-440000022-2-2000022-2-20-22-220000000000000000000000000000
χ524444-4-444-4-40000-4400-4400000-2-2220000-2-22202-22-20000000000000000000000000000
χ5344-4-44-4-444-4004-4000000-4400000000000000000000004i−4i000000000000000000000000
χ5444-4-44-4-444-4004-4000000-440000000000000000000000−4i4i000000000000000000000000
χ5544-4-44-4-444-400-440000004-4000000000000000000004i−4i00000000000000000000000000
χ5644-4-44-4-444-400-440000004-400000000000000000000−4i4i00000000000000000000000000
χ5744-4-4-4-44-44400004-400-440000022-2-20000-2-22202-2-220000000000000000000000000000
χ5844-4-4-4-44-44400004-400-4400000-2-222000022-2-20-222-20000000000000000000000000000
χ5944-4-4-4-44-4440000-44004-40000022-2-20000-2-2220-222-20000000000000000000000000000
χ6044-4-4-4-44-4440000-44004-400000-2-222000022-2-202-2-220000000000000000000000000000
χ618888-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6288-8-8-88-88-88000000000000000000000000000000000000000000000000000000000000
χ638-88i−8i0000004-400004i−4i0000000004-40000004i−4i000000000000000000000000000000000
χ648-88i−8i0000004-400004i−4i000000000-44000000−4i4i000000000000000000000000000000000
χ658-88i−8i000000-440000−4i4i00000004-40000004i−4i00000000000000000000000000000000000
χ668-88i−8i000000-440000−4i4i0000000-44000000−4i4i00000000000000000000000000000000000
χ678-8−8i8i0000004-40000−4i4i0000000004-4000000−4i4i000000000000000000000000000000000
χ688-8−8i8i0000004-40000−4i4i000000000-440000004i−4i000000000000000000000000000000000
χ698-8−8i8i000000-4400004i−4i00000004-4000000−4i4i00000000000000000000000000000000000
χ708-8−8i8i000000-4400004i−4i0000000-440000004i−4i00000000000000000000000000000000000

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