Finite Group Databasebeta

← Group #398732

Character table — Group #398732

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222444444444444888888888888888888888816161616161616161616161616161616
order12442222222444444422224444444444444444444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111
χ11111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ12111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111
χ1722222-222-2-2-222-2-2-22-222-2-222-2-200000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ1822222-222-2-2-222-2-2-22-222-2-222-2-20000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ1922222-222-2-2-222-2-2-22-2-2-222-2-22200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2022222-222-2-2-222-2-2-22-2-2-222-2-2220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ212222-222-22-2-22-222-2-2-2000000000000002i2i−2i−2i2i−2i2i−2i0000000022-2-20000000000000000
χ222222-222-22-2-22-222-2-2-2000000000000002i2i−2i−2i−2i2i−2i2i00000000-2-2220000000000000000
χ232222-222-22-2-22-222-2-2-200000000000000−2i−2i2i2i2i−2i2i−2i00000000-2-2220000000000000000
χ242222-222-22-2-22-222-2-2-200000000000000−2i−2i2i2i−2i2i−2i2i0000000022-2-20000000000000000
χ252222-22-22-22-2-222-22-2-22-22-22-22-200000000000000000000000000002i−2i0000002i−2i0000
χ262222-22-22-22-2-222-22-2-22-22-22-22-20000000000000000000000000000−2i2i000000−2i2i0000
χ272222-22-22-22-2-222-22-2-2-22-22-22-2200000000000000000000000000002i−2i000000−2i2i0000
χ282222-22-22-22-2-222-22-2-2-22-22-22-220000000000000000000000000000−2i2i0000002i−2i0000
χ292222-2-22-2-2222-2-2-22-22000000002222-2-200002-2-22000022-2-200000000000000000000
χ302222-2-22-2-2222-2-2-22-22000000002222-2-20000-222-20000-2-22200000000000000000000
χ312222-2-22-2-2222-2-2-22-2200000000-2-2-2-22200002-2-220000-2-22200000000000000000000
χ322222-2-22-2-2222-2-2-22-2200000000-2-2-2-2220000-222-2000022-2-200000000000000000000
χ332222-2-2-222-22-22-22-2-222-2-222-2-22000000000000000000000000000000002-20000002-2
χ342222-2-2-222-22-22-22-2-222-2-222-2-2200000000000000000000000000000000-22000000-22
χ352222-2-2-222-22-22-22-2-22-222-2-222-2000000000000000000000000000000002-2000000-22
χ362222-2-2-222-22-22-22-2-22-222-2-222-200000000000000000000000000000000-220000002-2
χ3722-2-222-2-2-2-2222-222-2-22-2-22-222-222-2-22-22-22-200000000000000000000000000000000
χ3822-2-222-2-2-2-2222-222-2-22-2-22-222-2-2-222-22-22-2200000000000000000000000000000000
χ3922-2-222-2-2-2-2222-222-2-2-222-22-2-2222-2-22-2-22-2200000000000000000000000000000000
χ4022-2-222-2-2-2-2222-222-2-2-222-22-2-22-2-222-222-22-200000000000000000000000000000000
χ4122-2-22-2-2-222-2222-2-2-222-22-2-22-220000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4222-2-22-2-2-222-2222-2-2-222-22-2-22-22000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4322-2-22-2-2-222-2222-2-2-22-22-222-22-20000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4422-2-22-2-2-222-2222-2-2-22-22-222-22-2000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4522-2-2-222-22-2-2-22-2-222222-2-2-2-222000000000000000000000000002i−2i0000002i−2i000000
χ4622-2-2-222-22-2-2-22-2-222222-2-2-2-22200000000000000000000000000−2i2i000000−2i2i000000
χ4722-2-2-222-22-2-2-22-2-2222-2-22222-2-2000000000000000000000000002i−2i000000−2i2i000000
χ4822-2-2-222-22-2-2-22-2-2222-2-22222-2-200000000000000000000000000−2i2i0000002i−2i000000
χ4922-2-2-22-22-22-22-2-22-222000000000000002i−2i−2i2i00002-22-22i−2i−2i2i00000000000000000000
χ5022-2-2-22-22-22-22-2-22-222000000000000002i−2i−2i2i0000-22-22−2i2i2i−2i00000000000000000000
χ5122-2-2-22-22-22-22-2-22-22200000000000000−2i2i2i−2i00002-22-2−2i2i2i−2i00000000000000000000
χ5222-2-2-22-22-22-22-2-22-22200000000000000−2i2i2i−2i0000-22-222i−2i−2i2i00000000000000000000
χ5322-2-2-2-22-2-222-2222-22-22222-2-2-2-20000000000000000000000000000002i−2i0000002i−2i00
χ5422-2-2-2-22-2-222-2222-22-22222-2-2-2-2000000000000000000000000000000−2i2i000000−2i2i00
χ5522-2-2-2-22-2-222-2222-22-2-2-2-2-222220000000000000000000000000000002i−2i000000−2i2i00
χ5622-2-2-2-22-2-222-2222-22-2-2-2-2-22222000000000000000000000000000000−2i2i0000002i−2i00
χ5722-2-2-2-2-222-222-22-222-20000000022-2-2-22000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ5822-2-2-2-2-222-222-22-222-20000000022-2-2-2200000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ5922-2-2-2-2-222-222-22-222-200000000-2-2222-2000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ6022-2-2-2-2-222-222-22-222-200000000-2-2222-200000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ61444444-4-4-4-44-4-44-4-44400000000000000000000000000000000000000000000000000
χ6244444-4-4-444-4-4-4-4444-400000000000000000000000000000000000000000000000000
χ6344-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000
χ6444-4-44-444-4-4-4-4-4444-4400000000000000000000000000000000000000000000000000
χ658-88i−8i00000000000000000000004-44i−4i00000000000000000000000000000000000000
χ668-88i−8i0000000000000000000000-44−4i4i00000000000000000000000000000000000000
χ678-8−8i8i00000000000000000000004-4−4i4i00000000000000000000000000000000000000
χ688-8−8i8i0000000000000000000000-444i−4i00000000000000000000000000000000000000

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