Finite Group Databasebeta

← Group #417441

Character table — Group #417441

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order12442222222444444444444444448888888888888888888888884444444488888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ9111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ10111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1
χ12111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ17222222-2-22-2-22222222-2-2-2-222-2-2-2-20000000022-2-222-2-2000000000000000000000000
χ18222222-2-22-2-22222222-2-2-2-222-2-2-2-200000000-2-222-2-222000000000000000000000000
χ19222222-2-22-2-22-2-2-2-222-2-2-2-2-2-222220000000022-2-2-2-222000000000000000000000000
χ20222222-2-22-2-22-2-2-2-222-2-2-2-2-2-2222200000000-2-22222-2-2000000000000000000000000
χ2122222-22-2-22-2-200002-22-22-200000000002i2i−2i−2i00002i−2i2i−2i22-2-200000000000000000000
χ2222222-22-2-22-2-200002-22-22-200000000002i2i−2i−2i0000−2i2i−2i2i-2-22200000000000000000000
χ2322222-22-2-22-2-200002-22-22-20000000000−2i−2i2i2i00002i−2i2i−2i-2-22200000000000000000000
χ2422222-22-2-22-2-200002-22-22-20000000000−2i−2i2i2i0000−2i2i−2i2i22-2-200000000000000000000
χ2522222-2-22-2-22-200002-2-22-220000002i2i−2i−2i000000002i−2i−2i2i000022-2-20000000000000000
χ2622222-2-22-2-22-200002-2-22-220000002i2i−2i−2i00000000−2i2i2i−2i0000-2-2220000000000000000
χ2722222-2-22-2-22-200002-2-22-22000000−2i−2i2i2i000000002i−2i−2i2i0000-2-2220000000000000000
χ2822222-2-22-2-22-200002-2-22-22000000−2i−2i2i2i00000000−2i2i2i−2i000022-2-20000000000000000
χ292222-222-2-2-22-20000-222-2-2200000000002i−2i2i−2i2i−2i2i−2i000000002-22-20000000000000000
χ302222-222-2-2-22-20000-222-2-2200000000002i−2i2i−2i−2i2i−2i2i00000000-22-220000000000000000
χ312222-222-2-2-22-20000-222-2-220000000000−2i2i−2i2i2i−2i2i−2i00000000-22-220000000000000000
χ322222-222-2-2-22-20000-222-2-220000000000−2i2i−2i2i−2i2i−2i2i000000002-22-20000000000000000
χ332222-22-22-22-2-20000-22-222-20000002i−2i2i−2i00002i−2i−2i2i00002-22-200000000000000000000
χ342222-22-22-22-2-20000-22-222-20000002i−2i2i−2i0000−2i2i2i−2i0000-22-2200000000000000000000
χ352222-22-22-22-2-20000-22-222-2000000−2i2i−2i2i00002i−2i−2i2i0000-22-2200000000000000000000
χ362222-22-22-22-2-20000-22-222-2000000−2i2i−2i2i0000−2i2i2i−2i00002-22-200000000000000000000
χ372222-2-2222-2-222222-2-222-2-2-2-222-2-22-2-222-2-2200000000000000000000000000000000
χ382222-2-2222-2-222222-2-222-2-2-2-222-2-2-222-2-222-200000000000000000000000000000000
χ392222-2-2222-2-22-2-2-2-2-2-222-2-222-2-2222-2-22-222-200000000000000000000000000000000
χ402222-2-2222-2-22-2-2-2-2-2-222-2-222-2-222-222-22-2-2200000000000000000000000000000000
χ412222-2-2-2-222222222-2-2-2-222-2-2-2-22200000000000000002-2-22-222-20000000000000000
χ422222-2-2-2-222222222-2-2-2-222-2-2-2-2220000000000000000-222-22-2-220000000000000000
χ432222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-200000000000000002-2-222-2-220000000000000000
χ442222-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-20000000000000000-222-2-222-20000000000000000
χ4522-2-22-22-2-22-222i2i−2i−2i-22-22-222i−2i2i−2i2i−2i0000000000000000000000002-20000002i−2i000000
χ4622-2-22-22-2-22-222i2i−2i−2i-22-22-222i−2i2i−2i2i−2i000000000000000000000000-22000000−2i2i000000
χ4722-2-22-22-2-22-22−2i−2i2i2i-22-22-22−2i2i−2i2i−2i2i0000000000000000000000002-2000000−2i2i000000
χ4822-2-22-22-2-22-22−2i−2i2i2i-22-22-22−2i2i−2i2i−2i2i000000000000000000000000-220000002i−2i000000
χ4922-2-22-2-22-2-2222i2i−2i−2i-222-22-22i−2i−2i2i−2i2i00000000000000000000000000002-20000002i−2i00
χ5022-2-22-2-22-2-2222i2i−2i−2i-222-22-22i−2i−2i2i−2i2i0000000000000000000000000000-22000000−2i2i00
χ5122-2-22-2-22-2-222−2i−2i2i2i-222-22-2−2i2i2i−2i2i−2i00000000000000000000000000002-2000000−2i2i00
χ5222-2-22-2-22-2-222−2i−2i2i2i-222-22-2−2i2i2i−2i2i−2i0000000000000000000000000000-220000002i−2i00
χ5322-2-2-222-2-2-2222i2i−2i−2i2-2-222-2−2i2i2i−2i−2i2i000000000000000000000000002-20000002i−2i0000
χ5422-2-2-222-2-2-2222i2i−2i−2i2-2-222-2−2i2i2i−2i−2i2i00000000000000000000000000-22000000−2i2i0000
χ5522-2-2-222-2-2-222−2i−2i2i2i2-2-222-22i−2i−2i2i2i−2i000000000000000000000000002-2000000−2i2i0000
χ5622-2-2-222-2-2-222−2i−2i2i2i2-2-222-22i−2i−2i2i2i−2i00000000000000000000000000-220000002i−2i0000
χ5722-2-2-22-22-22-222i2i−2i−2i2-22-2-22−2i2i−2i2i2i−2i0000000000000000000000000000002-20000002i−2i
χ5822-2-2-22-22-22-222i2i−2i−2i2-22-2-22−2i2i−2i2i2i−2i000000000000000000000000000000-22000000−2i2i
χ5922-2-2-22-22-22-22−2i−2i2i2i2-22-2-222i−2i2i−2i−2i2i0000000000000000000000000000002-2000000−2i2i
χ6022-2-2-22-22-22-22−2i−2i2i2i2-22-2-222i−2i2i−2i−2i2i000000000000000000000000000000-220000002i−2i
χ6144-4-44444444-40000-4-4-4-4-4-40000000000000000000000000000000000000000000000
χ6244-4-444-4-44-4-4-40000-4-444440000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-4-4000044-4-4440000000000000000000000000000000000000000000000
χ6444-4-4-4-4-4-4444-400004444-4-40000000000000000000000000000000000000000000000
χ658-88i−8i000000004+4i−4−4i4−4i−4+4i0000000000000000000000000000000000000000000000000000
χ668-88i−8i00000000−4−4i4+4i−4+4i4−4i0000000000000000000000000000000000000000000000000000
χ678-8−8i8i000000004−4i−4+4i4+4i−4−4i0000000000000000000000000000000000000000000000000000
χ688-8−8i8i00000000−4+4i4−4i−4−4i4+4i0000000000000000000000000000000000000000000000000000

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