Finite Group Databasebeta

← Group #358348

Character table — Group #358348

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222222288888888888888888888888888881111222222222222228888888888888888888888888888
order12442222222444444444444444444444444444888888882244222222244444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ1111111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222-2-22-2-22-222-2-2-200000000000000002-22-200000000222222-2-22-2-22-222-2-2-200000000000000002-22-200000000
χ18222222-2-22-2-22-222-2-2-20000000000000000-22-2200000000222222-2-22-2-22-222-2-2-20000000000000000-22-2200000000
χ1922222-2-2-2-2222-2-2-22-2200000000000000002i−2i−2i2i0000000022222-2-2-2-2222-2-2-22-2200000000000000002i−2i−2i2i00000000
χ2022222-2-2-2-2222-2-2-22-220000000000000000−2i2i2i−2i0000000022222-2-2-2-2222-2-2-22-220000000000000000−2i2i2i−2i00000000
χ212222-222-2-22-2-222-2-2-22000000000000000000002i−2i2i−2i00002222-222-2-22-2-222-2-2-22000000000000000000002i−2i2i−2i0000
χ222222-222-2-22-2-222-2-2-2200000000000000000000−2i2i−2i2i00002222-222-2-22-2-222-2-2-2200000000000000000000−2i2i−2i2i0000
χ232222-22-22-2-22-2-22-222-2000000002i−2i2i−2i00000000000000002222-22-22-2-22-2-22-222-2000000002i−2i2i−2i0000000000000000
χ242222-22-22-2-22-2-22-222-200000000−2i2i−2i2i00000000000000002222-22-22-2-22-2-22-222-200000000−2i2i−2i2i0000000000000000
χ252222-2-22-22-22-22-222-2-2000000000000000000002i−2i−2i2i00002222-2-22-22-22-22-222-2-2000000000000000000002i−2i−2i2i0000
χ262222-2-22-22-22-22-222-2-200000000000000000000−2i2i2i−2i00002222-2-22-22-22-22-222-2-200000000000000000000−2i2i2i−2i0000
χ272222-2-2-2222-2-2-2-22-222000000002-2-2200000000000000002222-2-2-2222-2-2-2-22-222000000002-2-220000000000000000
χ282222-2-2-2222-2-2-2-22-22200000000-222-200000000000000002222-2-2-2222-2-2-2-22-22200000000-222-20000000000000000
χ2922-2-22222222-2-2-2-2-2-2-22-22-200000000000000000000000022-2-22222222-2-2-2-2-2-2-22-22-2000000000000000000000000
χ3022-2-22222222-2-2-2-2-2-2-2-22-2200000000000000000000000022-2-22222222-2-2-2-2-2-2-2-22-22000000000000000000000000
χ3122-2-222-2-22-2-2-22-2-22220000000000002i−2i2i−2i00000000000022-2-222-2-22-2-2-22-2-22220000000000002i−2i2i−2i000000000000
χ3222-2-222-2-22-2-2-22-2-2222000000000000−2i2i−2i2i00000000000022-2-222-2-22-2-2-22-2-2222000000000000−2i2i−2i2i000000000000
χ3322-2-22-222-2-2-2-2-2222-222i−2i−2i2i00000000000000000000000022-2-22-222-2-2-2-2-2222-222i−2i−2i2i000000000000000000000000
χ3422-2-22-222-2-2-2-2-2222-22−2i2i2i−2i00000000000000000000000022-2-22-222-2-2-2-2-2222-22−2i2i2i−2i000000000000000000000000
χ3522-2-22-2-2-2-222-2222-22-20000000000002i−2i−2i2i00000000000022-2-22-2-2-2-222-2222-22-20000000000002i−2i−2i2i000000000000
χ3622-2-22-2-2-2-222-2222-22-2000000000000−2i2i2i−2i00000000000022-2-22-2-2-2-222-2222-22-2000000000000−2i2i2i−2i000000000000
χ3722-2-2-222-2-22-22-2-2222-20000000000000000000000002i−2i2i−2i22-2-2-222-2-22-22-2-2222-20000000000000000000000002i−2i2i−2i
χ3822-2-2-222-2-22-22-2-2222-2000000000000000000000000−2i2i−2i2i22-2-2-222-2-22-22-2-2222-2000000000000000000000000−2i2i−2i2i
χ3922-2-2-22-22-2-2222-22-2-2200002i−2i2i−2i0000000000000000000022-2-2-22-22-2-2222-22-2-2200002i−2i2i−2i00000000000000000000
χ4022-2-2-22-22-2-2222-22-2-220000−2i2i−2i2i0000000000000000000022-2-2-22-22-2-2222-22-2-220000−2i2i−2i2i00000000000000000000
χ4122-2-2-2-22-22-222-22-2-2220000000000000000000000002-2-2222-2-2-2-22-22-222-22-2-2220000000000000000000000002-2-22
χ4222-2-2-2-22-22-222-22-2-222000000000000000000000000-222-222-2-2-2-22-22-222-22-2-222000000000000000000000000-222-2
χ4322-2-2-2-2-2222-2222-22-2-200002i−2i−2i2i0000000000000000000022-2-2-2-2-2222-2222-22-2-200002i−2i−2i2i00000000000000000000
χ4422-2-2-2-2-2222-2222-22-2-20000−2i2i2i−2i0000000000000000000022-2-2-2-2-2222-2222-22-2-20000−2i2i2i−2i00000000000000000000
χ458-88i−8i0000000000000000000000000000000000000000008-88i−8i000000000000000000000000000000000000000000
χ468-8−8i8i0000000000000000000000000000000000000000008-8−8i8i000000000000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ491111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ52111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ53111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ54111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5511111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-1-1-1-1-11-1-1111-1-1111-11−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii
χ5611111-111-1-1-111-1-1-11-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-1-1-1-11-1-1111-1-1111-11−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i
χ5711111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-1-1-1-11-1-1111-1-1111-11−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i
χ5811111-111-1-1-111-1-1-11-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-1-1-1-11-1-1111-1-1111-11−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii
χ5911111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-1-1-1-1-11-1-1111-1-1111-11ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i
χ6011111-111-1-1-111-1-1-11-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-1-1-1-11-1-1111-1-1111-11ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii
χ6111111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-1-1-1-11-1-1111-1-1111-11ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii
χ6211111-111-1-1-111-1-1-11-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-1-1-1-11-1-1111-1-1111-11ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i
χ63222222-2-22-2-22-222-2-2-200000000000000002-22-200000000-2-2-2-2-2-222-222-22-2-22220000000000000000-22-2200000000
χ64222222-2-22-2-22-222-2-2-20000000000000000-22-2200000000-2-2-2-2-2-222-222-22-2-222200000000000000002-22-200000000
χ6522222-2-2-2-2222-2-2-22-2200000000000000002i−2i−2i2i00000000-2-2-2-2-22222-2-2-2222-22-20000000000000000−2i2i2i−2i00000000
χ6622222-2-2-2-2222-2-2-22-220000000000000000−2i2i2i−2i00000000-2-2-2-2-22222-2-2-2222-22-200000000000000002i−2i−2i2i00000000
χ672222-222-2-22-2-222-2-2-22000000000000000000002i−2i2i−2i0000-2-2-2-22-2-222-222-2-2222-200000000000000000000−2i2i−2i2i0000
χ682222-222-2-22-2-222-2-2-2200000000000000000000−2i2i−2i2i0000-2-2-2-22-2-222-222-2-2222-2000000000000000000002i−2i2i−2i0000
χ692222-22-22-2-22-2-22-222-2000000002i−2i2i−2i0000000000000000-2-2-2-22-22-222-222-22-2-2200000000−2i2i−2i2i0000000000000000
χ702222-22-22-2-22-2-22-222-200000000−2i2i−2i2i0000000000000000-2-2-2-22-22-222-222-22-2-22000000002i−2i2i−2i0000000000000000
χ712222-2-22-22-22-22-222-2-2000000000000000000002i−2i−2i2i0000-2-2-2-222-22-22-22-22-2-22200000000000000000000−2i2i2i−2i0000
χ722222-2-22-22-22-22-222-2-200000000000000000000−2i2i2i−2i0000-2-2-2-222-22-22-22-22-2-222000000000000000000002i−2i−2i2i0000
χ732222-2-2-2222-2-2-2-22-222000000002-2-220000000000000000-2-2-2-2222-2-2-22222-22-2-200000000-222-20000000000000000
χ742222-2-2-2222-2-2-2-22-22200000000-222-20000000000000000-2-2-2-2222-2-2-22222-22-2-2000000002-2-220000000000000000
χ7522-2-22222222-2-2-2-2-2-2-22-22-2000000000000000000000000-2-222-2-2-2-2-2-2-22222222-22-22000000000000000000000000
χ7622-2-22222222-2-2-2-2-2-2-2-22-22000000000000000000000000-2-222-2-2-2-2-2-2-222222222-22-2000000000000000000000000
χ7722-2-222-2-22-2-2-22-2-22220000000000002i−2i2i−2i000000000000-2-222-2-222-2222-222-2-2-2000000000000−2i2i−2i2i000000000000
χ7822-2-222-2-22-2-2-22-2-2222000000000000−2i2i−2i2i000000000000-2-222-2-222-2222-222-2-2-20000000000002i−2i2i−2i000000000000
χ7922-2-22-222-2-2-2-2-2222-222i−2i−2i2i000000000000000000000000-2-222-22-2-222222-2-2-22-2−2i2i2i−2i000000000000000000000000
χ8022-2-22-222-2-2-2-2-2222-22−2i2i2i−2i000000000000000000000000-2-222-22-2-222222-2-2-22-22i−2i−2i2i000000000000000000000000
χ8122-2-22-2-2-2-222-2222-22-20000000000002i−2i−2i2i000000000000-2-222-22222-2-22-2-2-22-22000000000000−2i2i2i−2i000000000000
χ8222-2-22-2-2-2-222-2222-22-2000000000000−2i2i2i−2i000000000000-2-222-22222-2-22-2-2-22-220000000000002i−2i−2i2i000000000000
χ8322-2-2-222-2-22-22-2-2222-20000000000000000000000002i−2i2i−2i-2-2222-2-222-22-222-2-2-22000000000000000000000000−2i2i−2i2i
χ8422-2-2-222-2-22-22-2-2222-2000000000000000000000000−2i2i−2i2i-2-2222-2-222-22-222-2-2-220000000000000000000000002i−2i2i−2i
χ8522-2-2-22-22-2-2222-22-2-2200002i−2i2i−2i00000000000000000000-2-2222-22-222-2-2-22-222-20000−2i2i−2i2i00000000000000000000
χ8622-2-2-22-22-2-2222-22-2-220000−2i2i−2i2i00000000000000000000-2-2222-22-222-2-2-22-222-200002i−2i2i−2i00000000000000000000
χ8722-2-2-2-22-22-222-22-2-2220000000000000000000000002-2-22-2-22222-22-22-2-22-222-2-2000000000000000000000000-222-2
χ8822-2-2-2-22-22-222-22-2-222000000000000000000000000-222-2-2-22222-22-22-2-22-222-2-20000000000000000000000002-2-22
χ8922-2-2-2-2-2222-2222-22-2-200002i−2i−2i2i00000000000000000000-2-222222-2-2-22-2-2-22-2220000−2i2i2i−2i00000000000000000000
χ9022-2-2-2-2-2222-2222-22-2-20000−2i2i2i−2i00000000000000000000-2-222222-2-2-22-2-2-22-22200002i−2i−2i2i00000000000000000000
χ918-88i−8i000000000000000000000000000000000000000000-88−8i8i000000000000000000000000000000000000000000
χ928-8−8i8i000000000000000000000000000000000000000000-888i−8i000000000000000000000000000000000000000000

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