Finite Group Databasebeta

← Group #72240519

Character table — Group #72240519

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111222222444444444444444488888888888888161616161616161616161616161616161616161632323232323232323232323232323232
order1244222444222222224444444422222224444444224444444444888888884444888888888888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−iii−i−i
χ1011-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii−i−iii
χ1111-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11-1111-1-1-1-111ii−i−iii−i−i-1-111ii−i−i−i−iii−i−iii
χ1211-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-11-1111-1-1-1-111−i−iii−i−iii-1-111−i−iiiii−i−iii−i−i
χ1311-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-11-11-1-1-11111-1-1ii−i−iii−i−i-1-111−i−iiiii−i−i−i−iii
χ1411-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-11-11-1-1-11111-1-1−i−iii−i−iii-1-111ii−i−i−i−iiiii−i−i
χ1511-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11-11-1-111-1-111ii−i−iii−i−i11-1-1−i−iii−i−iiiii−i−i
χ1611-1-1111-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11-11-1-111-1-111−i−iii−i−iii11-1-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-222222222-2-2-2-2-22222-2-22222-20000-2-2-2-20000000000000000000000000000
χ1822222222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000
χ19222222222222-2-222-2-222-2-2-2-2222-2-20000-2-20000200000000000000000000000000002-22-20000
χ20222222222222-2-222-2-222-2-2-2-2222-2-20000-2-2000020000000000000000000000000000-22-220000
χ21222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2220000220000-2000000000000000000000000000000002i−2i2i−2i
χ22222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2220000220000-200000000000000000000000000000000−2i2i−2i2i
χ232222222222-2-22222-2-2-2-2-2-22222-22-200002-20000-20000000000002222-2-2-2-20000000000000000
χ242222222222-2-22222-2-2-2-2-2-22222-22-200002-20000-2000000000000-2-2-2-222220000000000000000
χ252222222222-2-222-2-2-2-2-2-2-2-222-2-22-220000-22000020000000000000000000000002-22-200000000
χ262222222222-2-222-2-2-2-2-2-2-2-222-2-22-220000-2200002000000000000000000000000-22-2200000000
χ272222222222-2-2-2-22222-2-222-2-222-2-220000-220000-222220000-2-2-2-2000000000000000000000000
χ282222222222-2-2-2-22222-2-222-2-222-2-220000-220000-2-2-2-2-200002222000000000000000000000000
χ292222222222-2-2-2-2-2-222-2-222-2-2-2-222-200002-200002000000000000000000002-22-2000000000000
χ302222222222-2-2-2-2-2-222-2-222-2-2-2-222-200002-20000200000000000000000000-22-22000000000000
χ3122-2-2222-2-2-22222-2-222-2-2-2-2-2-222-2222222-2-2-2-2-2-220000-2-2220000000000000000000000000000
χ3222-2-2222-2-2-22222-2-222-2-2-2-2-2-222-222-2-2-2-2-2-222222000022-2-20000000000000000000000000000
χ3322-2-2222-2-2-222-2-222-2-2-2-22222-2-22220000-2-20000-200000000000000000000000000002i−2i−2i2i0000
χ3422-2-2222-2-2-222-2-222-2-2-2-22222-2-22220000-2-20000-20000000000000000000000000000−2i2i2i−2i0000
χ3522-2-2222-2-2-222-2-2-2-2-2-2-2-2222222-2-2-200002200002000000000000000000000000000000002-2-22
χ3622-2-2222-2-2-222-2-2-2-2-2-2-2-2222222-2-2-20000220000200000000000000000000000000000000-222-2
χ3722-2-2222-2-2-2-2-22222-2-22222-2-2-2-2-2-2200002-2000020000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ3822-2-2222-2-2-2-2-22222-2-22222-2-2-2-2-2-2200002-200002000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ3922-2-2222-2-2-2-2-222-2-2-2-22222-2-22222-20000-220000-20000000000000000000000002i−2i−2i2i00000000
χ4022-2-2222-2-2-2-2-222-2-2-2-22222-2-22222-20000-220000-2000000000000000000000000−2i2i2i−2i00000000
χ4122-2-2222-2-2-2-2-2-2-2222222-2-222-2-2-22-20000-22000022-22-20000-2-222000000000000000000000000
χ4222-2-2222-2-2-2-2-2-2-2222222-2-222-2-2-22-20000-2200002-22-22000022-2-2000000000000000000000000
χ4322-2-2222-2-2-2-2-2-2-2-2-22222-2-222222-2200002-20000-2000000000000000000002-2-22000000000000
χ4422-2-2222-2-2-2-2-2-2-2-2-22222-2-222222-2200002-20000-200000000000000000000-222-2000000000000
χ4544444-4-4-4-440000004-4004-40000000000000000000000000000002-22-22-22-20000000000000000
χ4644444-4-4-4-440000004-4004-4000000000000000000000000000000-22-22-22-220000000000000000
χ4744444-4-4-4-44000000-4400-440000000000000000000000000000002-22-2-22-220000000000000000
χ4844444-4-4-4-44000000-4400-44000000000000000000000000000000-22-222-22-20000000000000000
χ494444-44-44-4-400004-4000000004-400022-2-20022-2-2000002-22-20000000000000000000000000000
χ504444-44-44-4-400004-4000000004-4000-2-22200-2-22200000-22-220000000000000000000000000000
χ514444-44-44-4-40000-4400000000-4400022-2-20022-2-200000-22-220000000000000000000000000000
χ524444-44-44-4-40000-4400000000-44000-2-22200-2-222000002-22-20000000000000000000000000000
χ534444-4-44-44-4004-4000000004-400000000000000002-2-2200002-22-2000000000000000000000000
χ544444-4-44-44-4004-4000000004-40000000000000000-222-20000-22-22000000000000000000000000
χ554444-4-44-44-400-4400000000-4400000000000000002-2-220000-22-22000000000000000000000000
χ564444-4-44-44-400-4400000000-440000000000000000-222-200002-22-2000000000000000000000000
χ5744-4-44-4-444-40000004-400-440000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5844-4-44-4-444-40000004-400-44000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5944-4-44-4-444-4000000-44004-40000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ6044-4-44-4-444-4000000-44004-4000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ6144-4-4-44-4-44400004-400000000-4400022-2-200-2-222000002-2-220000000000000000000000000000
χ6244-4-4-44-4-44400004-400000000-44000-2-2220022-2-200000-222-20000000000000000000000000000
χ6344-4-4-44-4-4440000-44000000004-400022-2-200-2-22200000-222-20000000000000000000000000000
χ6444-4-4-44-4-4440000-44000000004-4000-2-2220022-2-2000002-2-220000000000000000000000000000
χ6544-4-4-4-444-44004-400000000-44000000000000000022-2-200002-2-22000000000000000000000000
χ6644-4-4-4-444-44004-400000000-440000000000000000-2-2220000-222-2000000000000000000000000
χ6744-4-4-4-444-4400-44000000004-4000000000000000022-2-20000-222-2000000000000000000000000
χ6844-4-4-4-444-4400-44000000004-40000000000000000-2-22200002-2-22000000000000000000000000
χ698-88i−8i0000004-40000004i−4i000000000004-400004i−4i0000000000000000000000000000000000000
χ708-88i−8i0000004-40000004i−4i00000000000-440000−4i4i0000000000000000000000000000000000000
χ718-88i−8i000000-44000000−4i4i0000000004-400004i−4i000000000000000000000000000000000000000
χ728-88i−8i000000-44000000−4i4i000000000-440000−4i4i000000000000000000000000000000000000000
χ738-8−8i8i0000004-4000000−4i4i000000000004-40000−4i4i0000000000000000000000000000000000000
χ748-8−8i8i0000004-4000000−4i4i00000000000-4400004i−4i0000000000000000000000000000000000000
χ758-8−8i8i000000-440000004i−4i0000000004-40000−4i4i000000000000000000000000000000000000000
χ768-8−8i8i000000-440000004i−4i000000000-4400004i−4i000000000000000000000000000000000000000

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