Finite Group Databasebeta

← Group #425012

Character table — Group #425012

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244448888888888888888888888161616161616161616161616161616161616
order12442222222444444444442222444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1
χ3111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1
χ51111111111111111111111-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111
χ9111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ11111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-11111
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-1-1-111-1-1
χ1722222-2-2-2-22222-2-2-22-20000000000000022-2-2000022-2-2000000002-200000000
χ1822222-2-2-2-22222-2-2-22-20000000000000022-2-20000-2-22200000000-2200000000
χ1922222-2-2-2-22222-2-2-22-200000000000000-2-222000022-2-200000000-2200000000
χ2022222-2-2-2-22222-2-2-22-200000000000000-2-2220000-2-222000000002-200000000
χ212222-2-222-22-22-22-2-2-2200002-2002-20000000022-2-2000000002-2000000000000
χ222222-2-222-22-22-22-2-2-2200002-2002-200000000-2-22200000000-22000000000000
χ232222-2-222-22-22-22-2-2-220000-2200-220000000022-2-200000000-22000000000000
χ242222-2-222-22-22-22-2-2-220000-2200-2200000000-2-222000000002-2000000000000
χ252222-2-22-22-22-22-22-2-222222002-2002-2-2-2000000000000000000000000002-200
χ262222-2-22-22-22-22-22-2-22222200-2200-22-2-200000000000000000000000000-2200
χ272222-2-22-22-22-22-22-2-22-2-2-2-2002-2002-22200000000000000000000000000-2200
χ282222-2-22-22-22-22-22-2-22-2-2-2-200-2200-2222000000000000000000000000002-200
χ2922-2-2222-2-2-2-22222-2-2-200002-222-22-2-2000000000000002-20000000000000000
χ3022-2-2222-2-2-2-22222-2-2-200002-2-2-2-222200000000000000-220000000000000000
χ3122-2-2222-2-2-2-22222-2-2-20000-22222-2-2-200000000000000-220000000000000000
χ3222-2-2222-2-2-2-22222-2-2-20000-22-2-22-222000000000000002-20000000000000000
χ3322-2-22-2-2-2-222-2-2222-2222-2-2000000002-200002i−2i2i−2i0000002i−2i00000000000000
χ3422-2-22-2-2-2-222-2-2222-2222-2-2000000002-20000−2i2i−2i2i000000−2i2i00000000000000
χ3522-2-22-2-2-2-222-2-2222-22-2-22200000000-2200002i−2i2i−2i000000−2i2i00000000000000
χ3622-2-22-2-2-2-222-2-2222-22-2-22200000000-220000−2i2i−2i2i0000002i−2i00000000000000
χ3722-2-2-22-22-2-222-2-22-22222-2-200000000-22000000002i−2i2i−2i0000000000002i−2i0000
χ3822-2-2-22-22-2-222-2-22-22222-2-200000000-2200000000−2i2i−2i2i000000000000−2i2i0000
χ3922-2-2-22-22-2-222-2-22-222-2-222000000002-2000000002i−2i2i−2i000000000000−2i2i0000
χ4022-2-2-22-22-2-222-2-22-222-2-222000000002-200000000−2i2i−2i2i0000000000002i−2i0000
χ4122-2-2-22-2-222-2-222-2-222000000000000002i−2i2i−2i2i−2i−2i2i000000000000000000002-2
χ4222-2-2-22-2-222-2-222-2-222000000000000002i−2i2i−2i−2i2i2i−2i00000000000000000000-22
χ4322-2-2-22-2-222-2-222-2-22200000000000000−2i2i−2i2i2i−2i−2i2i00000000000000000000-22
χ4422-2-2-22-2-222-2-222-2-22200000000000000−2i2i−2i2i−2i2i2i−2i000000000000000000002-2
χ4522-2-2-2-222-22-2-22-2222-20000002-200-22002i−2i−2i2i0000000000000000002i−2i000000
χ4622-2-2-2-222-22-2-22-2222-20000002-200-2200−2i2i2i−2i000000000000000000−2i2i000000
χ4722-2-2-2-222-22-2-22-2222-2000000-22002-2002i−2i−2i2i000000000000000000−2i2i000000
χ4822-2-2-2-222-22-2-22-2222-2000000-22002-200−2i2i2i−2i0000000000000000002i−2i000000
χ4922-2-2-2-22-22-222-22-222-200002200-2-20000000000002i−2i−2i2i0000002i−2i0000000000
χ5022-2-2-2-22-22-222-22-222-200002200-2-2000000000000−2i2i2i−2i000000−2i2i0000000000
χ5122-2-2-2-22-22-222-22-222-20000-2-200220000000000002i−2i−2i2i000000−2i2i0000000000
χ5222-2-2-2-22-22-222-22-222-20000-2-20022000000000000−2i2i2i−2i0000002i−2i0000000000
χ534444444-4-4-4-4-4-4-4-444400000000000000000000000000000000000000000000
χ5444444-4-444-4-4-4-444-44-400000000000000000000000000000000000000000000
χ554444-44-44-4-44-444-44-4-400000000000000000000000000000000000000000000
χ564444-44-4-444-44-4-444-4-400000000000000000000000000000000000000000000
χ5744-4-44444444-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ5844-4-44-4-444-4-444-4-44-4400000000000000000000000000000000000000000000
χ598-88i−8i000000000000004-44i−4i0000000000000000000000000000000000000000
χ608-88i−8i00000000000000-44−4i4i0000000000000000000000000000000000000000
χ618-8−8i8i000000000000004-4−4i4i0000000000000000000000000000000000000000
χ628-8−8i8i00000000000000-444i−4i0000000000000000000000000000000000000000

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