Finite Group Databasebeta

← Group #122003

Character table — Group #122003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-11-11-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-11-11−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-111-1-11ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-111-1-111-1−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-11-11-11-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11-11-11-11ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-1-111-1-11−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-111-1-111-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-2222-2-2-22-222-2-222-2-222-2-200000000000000000000000000000000002-200-2200000000
χ2222222222-2-2-2-2222-2-2-22-222-2-222-2-222-2-20000000000000000000000000000000000-22002-200000000
χ2322222222-2-2-2-2222-2-2-22-2-2-222-2-222-2-222000000000000000000000000000000002-200-220000000000
χ2422222222-2-2-2-2222-2-2-22-2-2-222-2-222-2-22200000000000000000000000000000000-22002-20000000000
χ2522222222-2-2-2-2-2-2-2222-2222-2-222-2-2-2-222000000000000000000000000000000002200-2-20000000000
χ2622222222-2-2-2-2-2-2-2222-2222-2-222-2-2-2-22200000000000000000000000000000000-2-200220000000000
χ2722222222-2-2-2-2-2-2-2222-22-2-222-2-22222-2-200000000000000000000000000000000002200-2-200000000
χ2822222222-2-2-2-2-2-2-2222-22-2-222-2-22222-2-20000000000000000000000000000000000-2-2002200000000
χ292222-2-2-2-222-2-222-222-2-2-222-2-2-2-2222-22-200000000000000000000000000000000000000002-22-20000
χ302222-2-2-2-222-2-222-222-2-2-222-2-2-2-2222-22-20000000000000000000000000000000000000000-22-220000
χ312222-2-2-2-222-2-222-222-2-2-2-2-22222-2-2-22-22000000000000000000000000000000000000000000002-22-2
χ322222-2-2-2-222-2-222-222-2-2-2-2-22222-2-2-22-2200000000000000000000000000000000000000000000-22-22
χ332222-2-2-2-222-2-2-2-22-2-222222-2-2-2-222-22-22000000000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-222-2-2-2-22-2-222222-2-2-2-222-22-2200000000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-2-22-2-2222-2-22222-2-22-22-200000000000000000000000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-222-2-2-2-22-2-2222-2-22222-2-22-22-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-2-2-2-22222-2-2-22-222222-2-2-2-22-2-2200000000000000000000000022-2-222-2-20000000000000000
χ382222-2-2-2-2-2-22222-2-2-22-222222-2-2-2-22-2-22000000000000000000000000-2-222-2-2220000000000000000
χ392222-2-2-2-2-2-22222-2-2-22-22-2-2-2-22222-222-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ402222-2-2-2-2-2-22222-2-2-22-22-2-2-2-22222-222-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ412222-2-2-2-2-2-222-2-2222-22-22222-2-2-2-2-222-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ422222-2-2-2-2-2-222-2-2222-22-22222-2-2-2-2-222-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ432222-2-2-2-2-2-222-2-2222-22-2-2-2-2-222222-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ442222-2-2-2-2-2-222-2-2222-22-2-2-2-2-222222-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4522-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2i2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-22-22-22-22-2000000002i−2i2i−2i2i−2i2i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2i2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i002i−2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5022-2-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2i2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5122-2-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i002i−2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ5222-2-22-22-22-22-200000000−2i2i−2i2i−2i2i−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2i2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ5322-2-2-22-22-222-2000000002i−2i2i−2i−2i2i−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i2i−2i00002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5422-2-2-22-22-222-2000000002i−2i2i−2i−2i2i−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−2i2i0000-22−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5522-2-2-22-22-222-2000000002i−2i2i−2i−2i2i−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i2i−2i00002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ5622-2-2-22-22-222-2000000002i−2i2i−2i−2i2i−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−2i2i0000-221−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ5722-2-2-22-22-222-200000000−2i2i−2i2i2i−2i2i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i2i−2i0000-22−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ5822-2-2-22-22-222-200000000−2i2i−2i2i2i−2i2i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−2i2i00002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ5922-2-2-22-22-222-200000000−2i2i−2i2i2i−2i2i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i2i−2i0000-221+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ6022-2-2-22-22-222-200000000−2i2i−2i2i2i−2i2i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−2i2i00002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ6144-4-44-44-4-44-44000000004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-44-4400000000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4-44000000004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ6444-4-4-44-444-4-4400000000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ654-44-444-4-400000004-440-40000000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ664-44-444-4-400000004-440-4000000000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ674-44-444-4-40000000-44-4040000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ684-44-444-4-40000000-44-404000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ694-44-4-4-44400000004-4-4040000000000002-22-2-22-22-22-222-22-200000000000000000000000000000000
χ704-44-4-4-44400000004-4-404000000000000-22-222-22-22-22-2-22-2200000000000000000000000000000000
χ714-44-4-4-4440000000-4440-40000000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ724-44-4-4-4440000000-4440-4000000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ734-4-444-4-4400004-44000-400000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ744-4-444-4-4400004-44000-40000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ754-4-444-4-440000-44-4000400000000000002-2-222-2-222-2-222-2-2200000000000000000000000000000000
χ764-4-444-4-440000-44-400040000000000000-222-2-222-2-222-2-222-200000000000000000000000000000000
χ774-4-44-444-400004-4-4000400000000000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ784-4-44-444-400004-4-400040000000000000-222-22-2-222-2-22-222-200000000000000000000000000000000
χ794-4-44-444-40000-444000-400000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ804-4-44-444-40000-444000-40000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000

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