Finite Group Databasebeta

← Group #72316523

Character table — Group #72316523

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111111122222222222244444444888888888888888888888888161616161616161616161616161616161616161616161616323232323232323232323232
order1222444422222244444422444444222444444444444444444444222244444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ91111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-11111-1-1-1-1111-111-1-1-1-11-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-11111-1-1-1-111-11-1-111-1-1-1111-1-111-1-111-1-1-1-111-1-111-1-111
χ111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1111-1-1-11111-1-1-1-11111-1-1-1-111-1-111
χ121111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-11111-11-1-11111-1-1-1-111-1-11111-1-111-1-1
χ131111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11111-1-1-11111-1-1-1-1111-111-1-1-1-11-1-1-111-1-111-1-111-1-111-1-11111-1-1
χ141111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11111-1-1-11111-1-1-1-111-11-1-111-1-1-11-1-111-1-111-1-11111-1-111-1-1-1-111
χ151111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11-111-1-1111-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ161111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-11-1-11111-1111-1-1-1-11111-1-111-1-1-1-11111-1-1
χ172222222222222222222222-2-222-2-22-2-2-2-2222222222-2-2000000000000000000000000-2-2-2-20000000000000000
χ182222222222222222222222-2-222-2-22-2-2-2-2-2-2-2-2-2-2-2-22-2-200000000000000000000000022220000000000000000
χ1922222222222222222222-2-222-2-222-2-2-22200000000-2-2-222222222-2-2000000-2-200000000000000000000000000
χ2022222222222222222222-2-222-2-222-2-2-22200000000-2-2-2-2-2-2-2-2-2-2-2220000002200000000000000000000000000
χ2122222222222222222222-2-2-2-2-2-2-2-2-222-2-200000000-2220000000000000000000022220000-2-2-2-2000000000000
χ2222222222222222222222-2-2-2-2-2-2-2-2-222-2-200000000-22200000000000000000000-2-2-2-200002222000000000000
χ2322222222-2-2-222-222-2-2-2-222222222-22-2-2-200000000-22-200000000002-22-22-200-22000000000000000000000000
χ2422222222-2-2-222-222-2-2-2-222222222-22-2-2-200000000-22-20000000000-22-22-22002-2000000000000000000000000
χ2522222222-2-2-222-222-2-2-2-222-2-222-2-2-2-222200000000-2-22000000000000000000000000000000002-22-200000000
χ2622222222-2-2-222-222-2-2-2-222-2-222-2-2-2-222200000000-2-2200000000000000000000000000000000-22-2200000000
χ2722222222-2-2-222-222-2-2-2-2-2-222-2-2222-22-2-2000000002-2200000000000000000000000000000000000000002-22-2
χ2822222222-2-2-222-222-2-2-2-2-2-222-2-2222-22-2-2000000002-220000000000000000000000000000000000000000-22-22
χ2922222222-2-2-222-222-2-2-2-2-2-2-2-2-2-2-2-222-2220000000022-20000000000000000000000000000000000002i−2i2i−2i0000
χ3022222222-2-2-222-222-2-2-2-2-2-2-2-2-2-2-2-222-2220000000022-2000000000000000000000000000000000000−2i2i−2i2i0000
χ312222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22-2-2-222222-2-2-2-2-222000000000000000000000000-2-2220000000000000000
χ322222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22-2-2-22-2-2-2-22222-22200000000000000000000000022-2-20000000000000000
χ332222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-222-22000000002-2-20000000000000000000022-2-20000-2-222000000000000
χ342222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-222-22000000002-2-200000000000000000000-2-222000022-2-2000000000000
χ352222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-2-22-2000000002222222-2-2-2-2-2-20000002200000000000000000000000000
χ362222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-2-22-200000000222-2-2-2-2222222000000-2-200000000000000000000000000
χ372222-2-2-2-2-2-2-222-2-2-222222222-2-2-2-2-2-222-20000000022-2000000000000000000000000000000002-2-2200000000
χ382222-2-2-2-2-2-2-222-2-2-222222222-2-2-2-2-2-222-20000000022-200000000000000000000000000000000-222-200000000
χ392222-2-2-2-2-2-2-222-2-2-2222222-2-2-2-222-22-2-22000000002-220000000000222-2-2200-2-2000000000000000000000000
χ402222-2-2-2-2-2-2-222-2-2-2222222-2-2-2-222-22-2-22000000002-220000000000-2-2-222-20022000000000000000000000000
χ412222-2-2-2-2-2-2-222-2-2-22222-2-22222-2-222-22-200000000-2-220000000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-2-222-2-2-22222-2-22222-2-222-22-200000000-2-22000000000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-222-2-2-22222-2-2-2-222222-22-2200000000-22-200000000000000000000000000000000000000002-2-22
χ442222-2-2-2-2-2-2-222-2-2-22222-2-2-2-222222-22-2200000000-22-20000000000000000000000000000000000000000-222-2
χ45444444444-4-4-4-44-4-444-4-4000000000000000000000000000000000022-2-2-2-20022000000000000000000000000
χ46444444444-4-4-4-44-4-444-4-40000000000000000000000000000000000-2-2222200-2-2000000000000000000000000
χ4744444444-444-4-4-4-4-4-4-44400000000000000000000000000000000002-2-22-2200-22000000000000000000000000
χ4844444444-444-4-4-4-4-4-4-4440000000000000000000000000000000000-222-22-2002-2000000000000000000000000
χ494444-4-4-4-44-4-4-4-4444-4-44400000000000000000000000000000000002-2-2-222002-2000000000000000000000000
χ504444-4-4-4-44-4-4-4-4444-4-4440000000000000000000000000000000000-2222-2-200-22000000000000000000000000
χ514444-4-4-4-4-444-4-4-44444-4-4000000000000000000000000000000000022-222-200-2-2000000000000000000000000
χ524444-4-4-4-4-444-4-4-44444-4-40000000000000000000000000000000000-2-22-2-220022000000000000000000000000
χ5344-4-44i4i−4i−4i0004-404i−4i0000004i−4i004-40000022-2-22i2i−2i−2i0000000000000000000000000002-22i−2i0000000000000000
χ5444-4-44i4i−4i−4i0004-404i−4i0000004i−4i004-400000-2-222−2i−2i2i2i000000000000000000000000000-22−2i2i0000000000000000
χ5544-4-44i4i−4i−4i0004-404i−4i000000−4i4i00-440000022-2-22i2i−2i−2i000000000000000000000000000-22−2i2i0000000000000000
χ5644-4-44i4i−4i−4i0004-404i−4i000000−4i4i00-4400000-2-222−2i−2i2i2i0000000000000000000000000002-22i−2i0000000000000000
χ5744-4-44i4i−4i−4i000-440−4i4i00004-4004i−4i00000000000000000022-2-22i2i−2i−2i2-20000002i−2i00000000000000000000000000
χ5844-4-44i4i−4i−4i000-440−4i4i00004-4004i−4i000000000000000000-2-222−2i−2i2i2i-22000000−2i2i00000000000000000000000000
χ5944-4-44i4i−4i−4i000-440−4i4i0000-4400−4i4i00000000000000000022-2-22i2i−2i−2i-22000000−2i2i00000000000000000000000000
χ6044-4-44i4i−4i−4i000-440−4i4i0000-4400−4i4i000000000000000000-2-222−2i−2i2i2i2-20000002i−2i00000000000000000000000000
χ6144-4-4−4i−4i4i4i0004-40−4i4i0000004i−4i00-440000022-2-2−2i−2i2i2i000000000000000000000000000-222i−2i0000000000000000
χ6244-4-4−4i−4i4i4i0004-40−4i4i0000004i−4i00-4400000-2-2222i2i−2i−2i0000000000000000000000000002-2−2i2i0000000000000000
χ6344-4-4−4i−4i4i4i0004-40−4i4i000000−4i4i004-40000022-2-2−2i−2i2i2i0000000000000000000000000002-2−2i2i0000000000000000
χ6444-4-4−4i−4i4i4i0004-40−4i4i000000−4i4i004-400000-2-2222i2i−2i−2i000000000000000000000000000-222i−2i0000000000000000
χ6544-4-4−4i−4i4i4i000-4404i−4i00004-400−4i4i00000000000000000022-2-2−2i−2i2i2i2-2000000−2i2i00000000000000000000000000
χ6644-4-4−4i−4i4i4i000-4404i−4i00004-400−4i4i000000000000000000-2-2222i2i−2i−2i-220000002i−2i00000000000000000000000000
χ6744-4-4−4i−4i4i4i000-4404i−4i0000-44004i−4i00000000000000000022-2-2−2i−2i2i2i-220000002i−2i00000000000000000000000000
χ6844-4-4−4i−4i4i4i000-4404i−4i0000-44004i−4i000000000000000000-2-2222i2i−2i−2i2-2000000−2i2i00000000000000000000000000
χ694-44-44i−4i4i−4i04-400000004i−4i00000000000002i−2i2i−2i2-22-20002-22-22i−2i2i−2i0000000000002i−2i2-200000000000000000000
χ704-44-44i−4i4i−4i04-400000004i−4i00000000000002i−2i2i−2i2-22-2000-22-22−2i2i−2i2i000000000000−2i2i-2200000000000000000000
χ714-44-44i−4i4i−4i04-400000004i−4i0000000000000−2i2i−2i2i-22-220002-22-22i−2i2i−2i000000000000−2i2i-2200000000000000000000
χ724-44-44i−4i4i−4i04-400000004i−4i0000000000000−2i2i−2i2i-22-22000-22-22−2i2i−2i2i0000000000002i−2i2-200000000000000000000
χ734-44-4−4i4i−4i4i04-40000000−4i4i00000000000002i−2i2i−2i-22-220002-22-2−2i2i−2i2i0000000000002i−2i-2200000000000000000000
χ744-44-4−4i4i−4i4i04-40000000−4i4i00000000000002i−2i2i−2i-22-22000-22-222i−2i2i−2i000000000000−2i2i2-200000000000000000000
χ754-44-4−4i4i−4i4i04-40000000−4i4i0000000000000−2i2i−2i2i2-22-20002-22-2−2i2i−2i2i000000000000−2i2i2-200000000000000000000
χ764-44-4−4i4i−4i4i04-40000000−4i4i0000000000000−2i2i−2i2i2-22-2000-22-222i−2i2i−2i0000000000002i−2i-2200000000000000000000
χ774-4-444-4-4440000-4004-40000000000000002i−2i−2i2i−2i2i2i−2i0002-2-222-2-22000000000000000000002i−2i2i−2i000000000000
χ784-4-444-4-4440000-4004-40000000000000002i−2i−2i2i−2i2i2i−2i000-222-2-222-200000000000000000000−2i2i−2i2i000000000000
χ794-4-444-4-4440000-4004-4000000000000000−2i2i2i−2i2i−2i−2i2i0002-2-222-2-2200000000000000000000−2i2i−2i2i000000000000
χ804-4-444-4-4440000-4004-4000000000000000−2i2i2i−2i2i−2i−2i2i000-222-2-222-2000000000000000000002i−2i2i−2i000000000000
χ814-4-44-444-440000-400-440000000000000002i−2i−2i2i2i−2i−2i2i0002-2-22-222-2000000000000000000002i−2i−2i2i000000000000
χ824-4-44-444-440000-400-440000000000000002i−2i−2i2i2i−2i−2i2i000-222-22-2-2200000000000000000000−2i2i2i−2i000000000000
χ834-4-44-444-440000-400-44000000000000000−2i2i2i−2i−2i2i2i−2i0002-2-22-222-200000000000000000000−2i2i2i−2i000000000000
χ844-4-44-444-440000-400-44000000000000000−2i2i2i−2i−2i2i2i−2i000-222-22-2-22000000000000000000002i−2i−2i2i000000000000
χ858-88-88i−8i8i−8i0-880000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8−8i8i−8i8i0-8800000008i−8i00000000000000000000000000000000000000000000000000000000000000000000
χ878-8-888-8-88-80000800-880000000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-888-8-800008008-80000000000000000000000000000000000000000000000000000000000000000000000

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