Finite Group Databasebeta

← Group #209892

Character table — Group #209892

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222444444444444444444444444888888888888888888888888161616161616161616161616
order12222222444444444444444444444444444444444444224444444444444488888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ611111111111111111111-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ911111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1711-111-1-1-1ii−i−i11-1-111-1-111-1-1ii−i−i11-1-1ii−i−ii−iii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i1-1i−i1-1i−i
χ1811-111-1-1-1ii−i−i11-1-111-1-111-1-1ii−i−i11-1-1ii−i−ii−iii−i−i1-11-1i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-11−ii-11−ii-11−ii
χ1911-111-1-1-1ii−i−i11-1-111-1-111-1-1ii−i−i-1-111−i−iiii−iii−i−i1-1-11−ii1-1i−i-1-111−i−iii11-1-1ii−i−i-11−ii1-1i−i-11−ii
χ2011-111-1-1-1ii−i−i11-1-111-1-111-1-1ii−i−i-1-111−i−iiii−iii−i−i1-1-11−ii1-1i−i-1-111−i−iii-1-111−i−iii1-1i−i-11−ii1-1i−i
χ2111-111-1-1-1ii−i−i11-1-111-1-1-1-111ii−i−i11-1-1ii−i−ii−i−i−iii1-11-1i−i-11−ii-1-111−i−iii11-1-1ii−i−i-11−ii-11−ii1-1i−i
χ2211-111-1-1-1ii−i−i11-1-111-1-1-1-111ii−i−i11-1-1ii−i−ii−i−i−iii1-11-1i−i-11−ii-1-111−i−iii-1-111−i−iii1-1i−i1-1i−i-11−ii
χ2311-111-1-1-1ii−i−i11-1-111-1-1-1-111ii−i−i-1-111−i−iiii−i−i−iii1-1-11−ii-11−ii11-1-1ii−i−i11-1-1ii−i−i1-1i−i-11−ii-11−ii
χ2411-111-1-1-1ii−i−i11-1-111-1-1-1-111ii−i−i-1-111−i−iiii−i−i−iii1-1-11−ii-11−ii11-1-1ii−i−i-1-111−i−iii-11−ii1-1i−i1-1i−i
χ2511-111-1-1-1−i−iii11-1-111-1-111-1-1−i−iii11-1-1−i−iii−ii−i−iii1-11-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ2611-111-1-1-1−i−iii11-1-111-1-111-1-1−i−iii11-1-1−i−iii−ii−i−iii1-11-1−ii1-1−ii11-1-1−i−iii-1-111ii−i−i-11i−i-11i−i-11i−i
χ2711-111-1-1-1−i−iii11-1-111-1-111-1-1−i−iii-1-111ii−i−i−ii−i−iii1-1-11i−i1-1−ii-1-111ii−i−i11-1-1−i−iii-11i−i1-1−ii-11i−i
χ2811-111-1-1-1−i−iii11-1-111-1-111-1-1−i−iii-1-111ii−i−i−ii−i−iii1-1-11i−i1-1−ii-1-111ii−i−i-1-111ii−i−i1-1−ii-11i−i1-1−ii
χ2911-111-1-1-1−i−iii11-1-111-1-1-1-111−i−iii11-1-1−i−iii−iiii−i−i1-11-1−ii-11i−i-1-111ii−i−i11-1-1−i−iii-11i−i-11i−i1-1−ii
χ3011-111-1-1-1−i−iii11-1-111-1-1-1-111−i−iii11-1-1−i−iii−iiii−i−i1-11-1−ii-11i−i-1-111ii−i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i
χ3111-111-1-1-1−i−iii11-1-111-1-1-1-111−i−iii-1-111ii−i−i−iiii−i−i1-1-11i−i-11i−i11-1-1−i−iii11-1-1−i−iii1-1−ii-11i−i-11i−i
χ3211-111-1-1-1−i−iii11-1-111-1-1-1-111−i−iii-1-111ii−i−i−iiii−i−i1-1-11i−i-11i−i11-1-1−i−iii-1-111ii−i−i-11i−i1-1−ii1-1−ii
χ332222222222222-22-22-22-200002-22-222222222-2-20000-2-2-2-2-2-200000000000000000000000000000000
χ342222222222222-22-22-22-200002-22-2-2-2-2-2-2-2-2-2-2-20000-2-2222200000000000000000000000000000000
χ35222222222222-22-22-22-222222-22-2200000000-2-22222-2-20000-2-2-2-20000000000000000000000000000
χ36222222222222-22-22-22-22-2-2-2-2-22-2200000000-2-2-2-2-2-2-2-2000022220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-20000-2-2-2-20000000022000022000000002-22-22-22-200000000000000000000
χ38222222222222-2-2-2-2-2-2-2-20000-2-2-2-2000000002200002200000000-22-22-22-2200000000000000000000
χ3922222222-2-2-2-22-22-22-22-20000-22-222222-2-2-2-2220000-2-2-2-22200000000000000000000000000000000
χ4022222222-2-2-2-22-22-22-22-20000-22-22-2-2-2-22222220000-2-222-2-200000000000000000000000000000000
χ4122222222-2-2-2-2-22-22-22-2222222-22-20000000022-2-2-2-2-2-20000-2-2220000000000000000000000000000
χ4222222222-2-2-2-2-22-22-22-22-2-2-2-22-22-200000000222222-2-2000022-2-20000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000-2-2000022000000002-22-2-22-2200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000-2-200002200000000-22-222-22-200000000000000000000
χ4522-222-2-2-22i2i−2i−2i2-2-222-2-2200002i−2i−2i2i22-2-22i2i−2i−2i−2i2i0000-22-22−2i2i00000000000000000000000000000000
χ4622-222-2-2-22i2i−2i−2i2-2-222-2-2200002i−2i−2i2i-2-222−2i−2i2i2i−2i2i0000-222-22i−2i00000000000000000000000000000000
χ4722-222-2-2-22i2i−2i−2i-222-2-222-222-2-2−2i2i2i−2i00000000−2i2i2i2i−2i−2i-220000-22−2i2i0000000000000000000000000000
χ4822-222-2-2-22i2i−2i−2i-222-2-222-2-2-222−2i2i2i−2i00000000−2i2i−2i−2i2i2i-2200002-22i−2i0000000000000000000000000000
χ4922-222-2-2-22i2i−2i−2i-2-222-2-2220000−2i−2i2i2i000000002i−2i00002-2000000002-2-222i−2i−2i2i00000000000000000000
χ5022-222-2-2-22i2i−2i−2i-2-222-2-2220000−2i−2i2i2i000000002i−2i00002-200000000-222-2−2i2i2i−2i00000000000000000000
χ5122-222-2-2-2−2i−2i2i2i2-2-222-2-220000−2i2i2i−2i22-2-2−2i−2i2i2i2i−2i0000-22-222i−2i00000000000000000000000000000000
χ5222-222-2-2-2−2i−2i2i2i2-2-222-2-220000−2i2i2i−2i-2-2222i2i−2i−2i2i−2i0000-222-2−2i2i00000000000000000000000000000000
χ5322-222-2-2-2−2i−2i2i2i-222-2-222-222-2-22i−2i−2i2i000000002i−2i−2i−2i2i2i-220000-222i−2i0000000000000000000000000000
χ5422-222-2-2-2−2i−2i2i2i-222-2-222-2-2-2222i−2i−2i2i000000002i−2i2i2i−2i−2i-2200002-2−2i2i0000000000000000000000000000
χ5522-222-2-2-2−2i−2i2i2i-2-222-2-22200002i2i−2i−2i00000000−2i2i00002-2000000002-2-22−2i2i2i−2i00000000000000000000
χ5622-222-2-2-2−2i−2i2i2i-2-222-2-22200002i2i−2i−2i00000000−2i2i00002-200000000-222-22i−2i−2i2i00000000000000000000
χ57444-4-4-4-444-44-40000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ58444-4-4-4-444-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ59444-4-4-4-44-44-440000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ60444-4-4-4-44-44-44000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ6144-4-4-444-44i−4i−4i4i0000000000000000000000000000000000000000000000002i−2i−2i2i-222-2000000000000
χ6244-4-4-444-44i−4i−4i4i000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ6344-4-4-444-4−4i4i4i−4i0000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ6444-4-4-444-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2000000000000
χ654-444-44-4-40000040-40-4044i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ664-444-44-4-40000040-40-404−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ674-444-44-4-400000-404040-40000000000000000004i−4i4i−4i00000000000000000000000000000000000000
χ684-444-44-4-400000-404040-4000000000000000000−4i4i−4i4i00000000000000000000000000000000000000
χ694-44-44-44-4000040-40-4040000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ704-44-44-44-4000040-40-404000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ714-44-44-44-40000-404040-400000000000004i−4i4i−4i00000000000000000000000000000000000000000000
χ724-44-44-44-40000-404040-40000000000000−4i4i−4i4i00000000000000000000000000000000000000000000
χ734-4-44-4-444000004040-40-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ744-4-44-4-444000004040-40-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ754-4-44-4-44400000-40-404040000000000000000004-4-4400000000000000000000000000000000000000
χ764-4-44-4-44400000-40-40404000000000000000000-444-400000000000000000000000000000000000000
χ774-4-4-444-4400004040-40-40000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ784-4-4-444-4400004040-40-4000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ794-4-4-444-440000-40-4040400000000000004-4-4400000000000000000000000000000000000000000000
χ804-4-4-444-440000-40-404040000000000000-444-400000000000000000000000000000000000000000000

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