Finite Group Databasebeta

← Group #375830

Character table — Group #375830

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222222224444444444444444444488888888888888888888888888888888881616161616161616
order12442222222444444422448888888888888888222224444444444444888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ9111111111111111111-1-1-1-11111111111111111-11111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ10111111111111111111-1-1-1-11111111111111111-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111
χ1711-1-11-1-111-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-111-11-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-11-1i−ii−i1-1
χ1811-1-11-1-111-1-111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-1111-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-111-11−ii−ii-11
χ1911-1-11-1-111-1-111-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-111-1-1-111ii−i−iii−i−i−i−iii−i−iii-1-1111-1i−i−ii-11
χ2011-1-11-1-111-1-111-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-111-11-11-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-11−iii−i1-1
χ2111-1-11-1-111-1-111-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-111-1-1-111−i−iii−i−iiiii−i−iii−i−i-1-1111-1−iii−i-11
χ2211-1-11-1-111-1-111-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-111-11-11-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-11i−i−ii1-1
χ2311-1-11-1-111-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-111-11-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-11-1−ii−ii1-1
χ2411-1-11-1-111-1-111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-1111-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-111-11i−ii−i-11
χ2511-1-11-1-111-1-111-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-11-1-11-11-1-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-11−ii−ii-11
χ2611-1-11-1-111-1-111-111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1-11-1-111−i−iii−i−iii−i−iii−i−iii-1-1111-1i−ii−i1-1
χ2711-1-11-1-111-1-111-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1-111-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111-11−iii−i1-1
χ2811-1-11-1-111-1-111-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-11-1-11-1111-1-1−i−iii−i−iiiii−i−iii−i−i11-1-11-1i−i−ii-11
χ2911-1-11-1-111-1-111-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-111-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-111-11i−i−ii1-1
χ3011-1-11-1-111-1-111-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-11-1-11-1111-1-1ii−i−iii−i−i−i−iii−i−iii11-1-11-1−iii−i-11
χ3111-1-11-1-111-1-111-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-11-1-11-11-1-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-11i−ii−i-11
χ3211-1-11-1-111-1-111-111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1-11-1-111ii−i−iii−i−iii−i−iii−i−i-1-1111-1−ii−ii1-1
χ33222222-2-2-22-2-2-2-2222-2000022-2-222-2-20000000000000000000000000000002-22-200002-22-200000000
χ34222222-2-2-22-2-2-2-2222-2000022-2-222-2-2000000000000000000000000000000-22-220000-22-2200000000
χ35222222-2-2-22-2-2-2-2222-20000-2-222-2-2220000000000000000000000000000002-22-20000-22-2200000000
χ36222222-2-2-22-2-2-2-2222-20000-2-222-2-222000000000000000000000000000000-22-2200002-22-200000000
χ3722222-2-222-2-2-2-22-2-22222220000000022-2-222-2-2-20000-2000000000000000000002-22-2000000000000
χ3822222-2-222-2-2-2-22-2-222222200000000-2-222-2-222-20000-200000000000000000000-22-22000000000000
χ3922222-2-222-2-2-2-22-2-222-2-2-2-20000000022-2-222-2-220000200000000000000000000-22-22000000000000
χ4022222-2-222-2-2-2-22-2-222-2-2-2-200000000-2-222-2-222200002000000000000000000002-22-2000000000000
χ412222-22-22-2-222-2-22-2-220000000000002-22-22-22-200000000002-22-200002-22-200000000000000000000
χ422222-22-22-2-222-2-22-2-220000000000002-22-22-22-20000000000-22-220000-22-2200000000000000000000
χ432222-22-22-2-222-2-22-2-22000000000000-22-22-22-2200000000002-22-20000-22-2200000000000000000000
χ442222-22-22-2-222-2-22-2-22000000000000-22-22-22-220000000000-22-2200002-22-200000000000000000000
χ452222-2-222-22-2-22-2-22-2200002-22-22-22-22-2-222-2-2202-2000-220000000000000000000000000000000000
χ462222-2-222-22-2-22-2-22-2200002-22-22-22-2-222-2-222-20-220002-20000000000000000000000000000000000
χ472222-2-222-22-2-22-2-22-220000-22-22-22-222-2-222-2-220-220002-20000000000000000000000000000000000
χ482222-2-222-22-2-22-2-22-220000-22-22-22-22-222-2-222-202-2000-220000000000000000000000000000000000
χ492222-2-2-2-22222-22-22-2-200002-2-222-2-22000000000002-2000-2200002-22-2000000000000000000000000
χ502222-2-2-2-22222-22-22-2-200002-2-222-2-2200000000000-220002-20000-22-22000000000000000000000000
χ512222-2-2-2-22222-22-22-2-20000-222-2-222-2000000000002-2000-220000-22-22000000000000000000000000
χ522222-2-2-2-22222-22-22-2-20000-222-2-222-200000000000-220002-200002-22-2000000000000000000000000
χ5322-2-22222222-2-2-2-2-2-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i20000-2000000000000000000002i−2i−2i2i000000000000
χ5422-2-22222222-2-2-2-2-2-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i20000-200000000000000000000−2i2i2i−2i000000000000
χ5522-2-22222222-2-2-2-2-2-2-2-2-222000000002i2i−2i−2i−2i−2i2i2i-20000200000000000000000000−2i2i2i−2i000000000000
χ5622-2-22222222-2-2-2-2-2-2-2-2-22200000000−2i−2i2i2i2i2i−2i−2i-200002000000000000000000002i−2i−2i2i000000000000
χ5722-2-22-22-2-2-22-2-2222-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000002i−2i−2i2i00002-2-2200000000
χ5822-2-22-22-2-2-22-2-2222-2200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−2i2i2i−2i0000-222-200000000
χ5922-2-22-22-2-2-22-2-2222-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000002i−2i−2i2i0000-222-200000000
χ6022-2-22-22-2-2-22-2-2222-220000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−2i2i2i−2i00002-2-2200000000
χ6122-2-2-222-22-2-22-2-2-222200002i−2i−2i2i−2i2i2i−2i0000000000022000-2-200002i−2i−2i2i000000000000000000000000
χ6222-2-2-222-22-2-22-2-2-222200002i−2i−2i2i−2i2i2i−2i00000000000-2-2000220000−2i2i2i−2i000000000000000000000000
χ6322-2-2-222-22-2-22-2-2-22220000−2i2i2i−2i2i−2i−2i2i0000000000022000-2-20000−2i2i2i−2i000000000000000000000000
χ6422-2-2-222-22-2-22-2-2-22220000−2i2i2i−2i2i−2i−2i2i00000000000-2-20002200002i−2i−2i2i000000000000000000000000
χ6522-2-2-22-22-2-22-222-222-200002i−2i2i−2i−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i022000-2-20000000000000000000000000000000000
χ6622-2-2-22-22-2-22-222-222-200002i−2i2i−2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i0-2-2000220000000000000000000000000000000000
χ6722-2-2-22-22-2-22-222-222-20000−2i2i−2i2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i0-2-2000220000000000000000000000000000000000
χ6822-2-2-22-22-2-22-222-222-20000−2i2i−2i2i2i−2i2i−2i−2i2i2i−2i2i−2i−2i2i022000-2-20000000000000000000000000000000000
χ6922-2-2-2-222-22-22-222-22-20000000000002i−2i2i−2i−2i2i−2i2i00000000002-2-2200002i−2i−2i2i00000000000000000000
χ7022-2-2-2-222-22-22-222-22-20000000000002i−2i2i−2i−2i2i−2i2i0000000000-222-20000−2i2i2i−2i00000000000000000000
χ7122-2-2-2-222-22-22-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i00000000002-2-220000−2i2i2i−2i00000000000000000000
χ7222-2-2-2-222-22-22-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000-222-200002i−2i−2i2i00000000000000000000
χ7344444-44-4-4-4444-4-4-44-400000000000000000000000000000000000000000000000000000000000000
χ744444-444-44-4-4-4444-4-4-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-444-4-4-44-4444-4-4-4400000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-4-4-4-4444-44-44-44400000000000000000000000000000000000000000000000000000000000000
χ778-88i−8i000000000000004-44i−4i0000000000000000000000000000000000000000000000000000000000
χ788-88i−8i00000000000000-44−4i4i0000000000000000000000000000000000000000000000000000000000
χ798-8−8i8i000000000000004-4−4i4i0000000000000000000000000000000000000000000000000000000000
χ808-8−8i8i00000000000000-444i−4i0000000000000000000000000000000000000000000000000000000000

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