Finite Group Databasebeta

← Group #370901

Character table — Group #370901

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444444444444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ9111111111111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ13111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ14111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ15111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ16111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1
χ1711-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i11-1-111-1-1ii−i−i1-1ii−i−iii−i−i11-1-1ii−i−i1-111-1-111-1-1ii−i−iii−i−i11-1-11-1i−i
χ1811-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i11-1-111-1-1ii−i−i1-1ii−i−iii−i−i11-1-1−i−iii1-1-1-111-1-111−i−iii−i−iii-1-111-11−ii
χ1911-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i11-1-111-1-1−i−iii-11ii−i−i−i−iii-1-111ii−i−i-1111-1-1-1-111−i−iiiii−i−i11-1-1-11−ii
χ2011-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i11-1-111-1-1−i−iii-11ii−i−i−i−iii-1-111−i−iii-11-1-11111-1-1ii−i−i−i−iii-1-1111-1i−i
χ2111-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i-1-111-1-111ii−i−i1-1−i−iii−i−iii-1-111ii−i−i1-111-1-1-1-111−i−iii−i−iii-1-1111-1i−i
χ2211-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i-1-111-1-111ii−i−i1-1−i−iii−i−iii-1-111−i−iii1-1-1-11111-1-1ii−i−iii−i−i11-1-1-11−ii
χ2311-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i-1-111-1-111−i−iii-11−i−iiiii−i−i11-1-1ii−i−i-1111-1-111-1-1ii−i−i−i−iii-1-111-11−ii
χ2411-1-11-1-111-11-1ii−i−i11-1-111-1-1iii−i−i−i-1-111-1-111−i−iii-11−i−iiiii−i−i11-1-1−i−iii-11-1-111-1-111−i−iiiii−i−i11-1-11-1i−i
χ2511-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii11-1-111-1-1ii−i−i-11−i−iiiii−i−i-1-111ii−i−i-11-1-11111-1-1−i−iiiii−i−i-1-1111-1−ii
χ2611-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii11-1-111-1-1ii−i−i-11−i−iiiii−i−i-1-111−i−iii-1111-1-1-1-111ii−i−i−i−iii11-1-1-11i−i
χ2711-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii11-1-111-1-1−i−iii1-1−i−iii−i−iii11-1-1ii−i−i1-1-1-111-1-111ii−i−iii−i−i-1-111-11i−i
χ2811-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii11-1-111-1-1−i−iii1-1−i−iii−i−iii11-1-1−i−iii1-111-1-111-1-1−i−iii−i−iii11-1-11-1−ii
χ2911-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii-1-111-1-111ii−i−i-11ii−i−i−i−iii11-1-1ii−i−i-11-1-111-1-111ii−i−i−i−iii11-1-11-1−ii
χ3011-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii-1-111-1-111ii−i−i-11ii−i−i−i−iii11-1-1−i−iii-1111-1-111-1-1−i−iiiii−i−i-1-111-11i−i
χ3111-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii-1-111-1-111−i−iii1-1ii−i−iii−i−i-1-111ii−i−i1-1-1-11111-1-1−i−iii−i−iii11-1-1-11i−i
χ3211-1-11-1-111-11-1−i−iii11-1-111-1-1−i−i−iiii-1-111-1-111−i−iii1-1ii−i−iii−i−i-1-111−i−iii1-111-1-1-1-111ii−i−iii−i−i-1-1111-1−ii
χ332222222222222222-2-2-2-2-2-2-2-22-2-22-2-20000000000000000002-22-22-22-2000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22-2-22-2-2000000000000000000-22-22-22-22000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-2220000000000000000002-22-2-22-22000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-222-222000000000000000000-22-222-22-2000000000000000000000000000000
χ3722222222-2-2-2-222222-22-22-22-2-22-2-22-2000000002-22-2220000000000000000-2-2000000000000000000000000
χ3822222222-2-2-2-222222-22-22-22-2-22-2-22-200000000-22-22-2-2000000000000000022000000000000000000000000
χ3922222222-2-2-2-22222-22-22-22-22-2-22-2-222222-2-2-2-20000002-22-200000000000000000000000000000000000000
χ4022222222-2-2-2-22222-22-22-22-22-2-22-2-22-2-2-2-22222000000-22-2200000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22-22-22-22-22-222-22000000002-22-2-2-2000000000000000022000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22-22-22-22-22-222-2200000000-22-22220000000000000000-2-2000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-22-22-22-2222-222-22222-2-2-2-2000000-22-2200000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-22-22-22-2222-222-2-2-2-2-222220000002-22-200000000000000000000000000000000000000
χ4522-2-22-2-222-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i0000000000000000002i−2i−2i2i2-2-22000000000000000000000000000000
χ4622-2-22-2-222-22-22i2i−2i−2i-2-222-2-2222i−2i−2i−2i2i2i000000000000000000−2i2i2i−2i-222-2000000000000000000000000000000
χ4722-2-22-2-222-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i0000000000000000002i−2i−2i2i-222-2000000000000000000000000000000
χ4822-2-22-2-222-22-2−2i−2i2i2i-2-222-2-222−2i2i2i2i−2i−2i000000000000000000−2i2i2i−2i2-2-22000000000000000000000000000000
χ4922-2-22-2-22-22-222i2i−2i−2i2-2-222-2-22−2i2i−2i2i−2i2i000000002i−2i−2i2i2-20000000000000000-22000000000000000000000000
χ5022-2-22-2-22-22-222i2i−2i−2i2-2-222-2-22−2i2i−2i2i−2i2i00000000−2i2i2i−2i-2200000000000000002-2000000000000000000000000
χ5122-2-22-2-22-22-222i2i−2i−2i-222-2-222-2−2i−2i2i2i2i−2i22-2-2-2-2220000002i−2i−2i2i00000000000000000000000000000000000000
χ5222-2-22-2-22-22-222i2i−2i−2i-222-2-222-2−2i−2i2i2i2i−2i-2-22222-2-2000000−2i2i2i−2i00000000000000000000000000000000000000
χ5322-2-22-2-22-22-22−2i−2i2i2i2-2-222-2-222i−2i2i−2i2i−2i000000002i−2i−2i2i-2200000000000000002-2000000000000000000000000
χ5422-2-22-2-22-22-22−2i−2i2i2i2-2-222-2-222i−2i2i−2i2i−2i00000000−2i2i2i−2i2-20000000000000000-22000000000000000000000000
χ5522-2-22-2-22-22-22−2i−2i2i2i-222-2-222-22i2i−2i−2i−2i2i22-2-2-2-222000000−2i2i2i−2i00000000000000000000000000000000000000
χ5622-2-22-2-22-22-22−2i−2i2i2i-222-2-222-22i2i−2i−2i−2i2i-2-22222-2-20000002i−2i−2i2i00000000000000000000000000000000000000
χ572-2222-2-2-22-2-220000-2-22-222-220000002i−2i2i−2i2i−2i2i−2i0000000000000000000000002i−2i2i−2i0000000000002-22-20000
χ582-2222-2-2-22-2-220000-2-22-222-220000002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2i2i−2i2i000000000000-22-220000
χ592-2222-2-2-22-2-220000-2-22-222-22000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002i−2i2i−2i000000000000-22-220000
χ602-2222-2-2-22-2-220000-2-22-222-22000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2i2i−2i2i0000000000002-22-20000
χ612-2222-2-2-2-222-200002-2-2-2-22220000002i−2i2i−2i−2i2i−2i2i0000000000000000002i−2i2i−2i000000000000002-22-200000000
χ622-2222-2-2-2-222-200002-2-2-2-22220000002i−2i2i−2i−2i2i−2i2i000000000000000000−2i2i−2i2i00000000000000-22-2200000000
χ632-2222-2-2-2-222-200002-2-2-2-2222000000−2i2i−2i2i2i−2i2i−2i0000000000000000002i−2i2i−2i00000000000000-22-2200000000
χ642-2222-2-2-2-222-200002-2-2-2-2222000000−2i2i−2i2i2i−2i2i−2i000000000000000000−2i2i−2i2i000000000000002-22-200000000
χ652-2-2-2222-222-2-20000-2-2-22222-20000002i−2i−2i2i2i−2i−2i2i0000000000000000000000002i−2i−2i2i0000000000002-2-220000
χ662-2-2-2222-222-2-20000-2-2-22222-20000002i−2i−2i2i2i−2i−2i2i000000000000000000000000−2i2i2i−2i000000000000-222-20000
χ672-2-2-2222-222-2-20000-2-2-22222-2000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000002i−2i−2i2i000000000000-222-20000
χ682-2-2-2222-222-2-20000-2-2-22222-2000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000−2i2i2i−2i0000000000002-2-220000
χ692-2-2-2222-2-2-22200002-222-22-2-20000002i−2i−2i2i−2i2i2i−2i0000000000000000002-2-2200000000000000−2i2i2i−2i00000000
χ702-2-2-2222-2-2-22200002-222-22-2-20000002i−2i−2i2i−2i2i2i−2i000000000000000000-222-2000000000000002i−2i−2i2i00000000
χ712-2-2-2222-2-2-22200002-222-22-2-2000000−2i2i2i−2i2i−2i−2i2i0000000000000000002-2-22000000000000002i−2i−2i2i00000000
χ722-2-2-2222-2-2-22200002-222-22-2-2000000−2i2i2i−2i2i−2i−2i2i000000000000000000-222-200000000000000−2i2i2i−2i00000000
χ734-4444-4-4-44-4-44000044-44-4-44-400000000000000000000000000000000000000000000000000000000000000
χ744-4444-4-4-4-444-40000-44444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ754-44-4-44-4400004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ764-44-4-44-4400004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ774-44-4-44-440000-44-44000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ784-44-4-44-440000-44-4400000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ794-4-44-4-44400004i−4i−4i4i000000000000000000000000000000000000000000000000002i−2i−2i2i-222-2000000000000
χ804-4-44-4-44400004i−4i−4i4i00000000000000000000000000000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ814-4-44-4-4440000−4i4i4i−4i000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ824-4-44-4-4440000−4i4i4i−4i00000000000000000000000000000000000000000000000000−2i2i2i−2i-222-2000000000000
χ834-4-4-4444-444-4-40000444-4-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4444-4-4-4440000-44-4-44-44400000000000000000000000000000000000000000000000000000000000000
χ85888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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