Finite Group Databasebeta

← Group #196368

Character table — Group #196368

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222444444444488888888888888881616161611111111222222224444444444888888888888888816161616
order12222222222244444444444444444444448888888824442222222222224444444444444444444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ911111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii1-11-1
χ1411111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i-11-1111111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i-11-11
χ1511111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii-11-1111111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii-11-11
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i1-11-111111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i1-11-1
χ17222222222222-2-2-2-2-2-22222-2-2-2-200000000000000000000222222222222-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000222222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000
χ1922222222-2-2-2-22222-2-222-2-2-2-2220000000000000000000022222222-2-2-2-22222-2-222-2-2-2-22200000000000000000000
χ2022222222-2-2-2-22222-2-2-2-22222-2-20000000000000000000022222222-2-2-2-22222-2-2-2-22222-2-200000000000000000000
χ2122-222-2-2-200002i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000000022-222-2-2-200002i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ2222-222-2-2-200002i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000000022-222-2-2-200002i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ2322-222-2-2-200002i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000000022-222-2-2-200002i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000
χ2422-222-2-2-200002i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000000022-222-2-2-200002i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000
χ2522-222-2-2-20000−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000000022-222-2-2-20000−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ2622-222-2-2-20000−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000000022-222-2-2-20000−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ2722-222-2-2-20000−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000000022-222-2-2-20000−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000
χ2822-222-2-2-20000−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000000022-222-2-2-20000−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000
χ292-2-22-22-222-22-222-2-22-2000000000000000000002i−2i2i−2i00002-2-22-22-222-22-222-2-22-2000000000000000000002i−2i2i−2i0000
χ302-2-22-22-222-22-222-2-22-200000000000000000000−2i2i−2i2i00002-2-22-22-222-22-222-2-22-200000000000000000000−2i2i−2i2i0000
χ312-2-22-22-222-22-2-2-222-2200000000000000002-22-2000000002-2-22-22-222-22-2-2-222-2200000000000000002-22-200000000
χ322-2-22-22-222-22-2-2-222-220000000000000000-22-22000000002-2-22-22-222-22-2-2-222-220000000000000000-22-2200000000
χ332-2-22-22-22-22-2222-2-2-2200000000000000002i−2i−2i2i000000002-2-22-22-22-22-2222-2-2-2200000000000000002i−2i−2i2i00000000
χ342-2-22-22-22-22-2222-2-2-220000000000000000−2i2i2i−2i000000002-2-22-22-22-22-2222-2-2-220000000000000000−2i2i2i−2i00000000
χ352-2-22-22-22-22-22-2-2222-2000000000000000000002-2-2200002-2-22-22-22-22-22-2-2222-2000000000000000000002-2-220000
χ362-2-22-22-22-22-22-2-2222-200000000000000000000-222-200002-2-22-22-22-22-22-2-2222-200000000000000000000-222-20000
χ37444-4-4-4-4444-4-40000000000000000000000000000000000444-4-4-4-4444-4-40000000000000000000000000000000000
χ38444-4-4-4-44-4-4440000000000000000000000000000000000444-4-4-4-44-4-4440000000000000000000000000000000000
χ3944-4-4-444-400000000000000004i−4i0000000000000000000044-4-4-444-400000000000000004i−4i00000000000000000000
χ4044-4-4-444-40000000000000000−4i4i0000000000000000000044-4-4-444-40000000000000000−4i4i00000000000000000000
χ414-444-4-44-400004i−4i−4i4i0000000000000000000000000000004-444-4-44-400004i−4i−4i4i000000000000000000000000000000
χ424-444-4-44-40000−4i4i4i−4i0000000000000000000000000000004-444-4-44-40000−4i4i4i−4i000000000000000000000000000000
χ434-44-444-4-400000000004i−4i000000000000000000000000004-44-444-4-400000000004i−4i00000000000000000000000000
χ444-44-444-4-40000000000−4i4i000000000000000000000000004-44-444-4-40000000000−4i4i00000000000000000000000000
χ454-4-4-44-4444-4-4400000000000000000000000000000000004-4-4-44-4444-4-440000000000000000000000000000000000
χ464-4-4-44-444-444-400000000000000000000000000000000004-4-4-44-444-444-40000000000000000000000000000000000
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
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4911111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-111-1
χ52111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-11
χ53111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-11
χ54111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-111-1
χ5511111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111−i−iii−i−iii−i−iii−i−iii-1-111
χ5611111111-1-1-1-1-1-1-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-1
χ5711111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-1
χ5811111111-1-1-1-1-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111ii−i−iii−i−iii−i−iii−i−i-1-111
χ5911111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii1-11-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i-11-11
χ6011111111-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i-11-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii1-11-1
χ6111111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii-11-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i1-11-1
χ6211111111-1-1-1-1-1-1-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i1-11-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii-11-11
χ63222222222222-2-2-2-2-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2222200000000000000000000
χ64222222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000
χ6522222222-2-2-2-22222-2-222-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222-2-200000000000000000000
χ6622222222-2-2-2-22222-2-2-2-22222-2-200000000000000000000-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000000000
χ6722-222-2-2-200002i−2i2i−2i00002-22i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000-2-22-2-22220000−2i2i−2i2i0000-22−2i2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ6822-222-2-2-200002i−2i2i−2i00002-22i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000-2-22-2-22220000−2i2i−2i2i0000-22−2i2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ6922-222-2-2-200002i−2i2i−2i0000-22−2i2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000-2-22-2-22220000−2i2i−2i2i00002-22i−2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000
χ7022-222-2-2-200002i−2i2i−2i0000-22−2i2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000-2-22-2-22220000−2i2i−2i2i00002-22i−2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000
χ7122-222-2-2-20000−2i2i−2i2i00002-2−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000-2-22-2-222200002i−2i2i−2i0000-222i−2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ7222-222-2-2-20000−2i2i−2i2i00002-2−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000-2-22-2-222200002i−2i2i−2i0000-222i−2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ7322-222-2-2-20000−2i2i−2i2i0000-222i−2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000-2-22-2-222200002i−2i2i−2i00002-2−2i2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000
χ7422-222-2-2-20000−2i2i−2i2i0000-222i−2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000-2-22-2-222200002i−2i2i−2i00002-2−2i2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000
χ752-2-22-22-222-22-222-2-22-2000000000000000000002i−2i2i−2i0000-222-22-22-2-22-22-2-222-2200000000000000000000−2i2i−2i2i0000
χ762-2-22-22-222-22-222-2-22-200000000000000000000−2i2i−2i2i0000-222-22-22-2-22-22-2-222-22000000000000000000002i−2i2i−2i0000
χ772-2-22-22-222-22-2-2-222-2200000000000000002-22-200000000-222-22-22-2-22-2222-2-22-20000000000000000-22-2200000000
χ782-2-22-22-222-22-2-2-222-220000000000000000-22-2200000000-222-22-22-2-22-2222-2-22-200000000000000002-22-200000000
χ792-2-22-22-22-22-2222-2-2-2200000000000000002i−2i−2i2i00000000-222-22-22-22-22-2-2-2222-20000000000000000−2i2i2i−2i00000000
χ802-2-22-22-22-22-2222-2-2-220000000000000000−2i2i2i−2i00000000-222-22-22-22-22-2-2-2222-200000000000000002i−2i−2i2i00000000
χ812-2-22-22-22-22-22-2-2222-2000000000000000000002-2-220000-222-22-22-22-22-222-2-2-2200000000000000000000-222-20000
χ822-2-22-22-22-22-22-2-2222-200000000000000000000-222-20000-222-22-22-22-22-222-2-2-22000000000000000000002-2-220000
χ83444-4-4-4-4444-4-40000000000000000000000000000000000-4-4-44444-4-4-4440000000000000000000000000000000000
χ84444-4-4-4-44-4-4440000000000000000000000000000000000-4-4-44444-444-4-40000000000000000000000000000000000
χ8544-4-4-444-400000000000000004i−4i00000000000000000000-4-4444-4-440000000000000000−4i4i00000000000000000000
χ8644-4-4-444-40000000000000000−4i4i00000000000000000000-4-4444-4-4400000000000000004i−4i00000000000000000000
χ874-444-4-44-400004i−4i−4i4i000000000000000000000000000000-44-4-444-440000−4i4i4i−4i000000000000000000000000000000
χ884-444-4-44-40000−4i4i4i−4i000000000000000000000000000000-44-4-444-4400004i−4i−4i4i000000000000000000000000000000
χ894-44-444-4-400000000004i−4i00000000000000000000000000-44-44-4-4440000000000−4i4i00000000000000000000000000
χ904-44-444-4-40000000000−4i4i00000000000000000000000000-44-44-4-44400000000004i−4i00000000000000000000000000
χ914-4-4-44-4444-4-440000000000000000000000000000000000-4444-44-4-4-444-40000000000000000000000000000000000
χ924-4-4-44-444-444-40000000000000000000000000000000000-4444-44-4-44-4-440000000000000000000000000000000000

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