Finite Group Databasebeta

← Group #161113

Character table — Group #161113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222444444444444444422224444444444444444444444444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-11111-1-1-111-1-1-1-1-11111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-11111-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-111-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-111-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iii−i−i−i−iiiiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-1111-1-1-1-1-1-1-1-111ii−i−iiiii−i−i−i−iii−i−i−i−i−i−iiiii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-1111-1-1-1-1-1-1-1-111−i−iii−i−i−i−iiiii−i−iiiiiii−i−i−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1-1-1-11-1-111111111-1-1ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1-1-1-11-1-111111111-1-1−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii
χ1711111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111-1-11-1-1-1-1-1-111-1-11111ii−i−iii−i−iii−i−i−i−iiiii−i−iii−i−ii−ii−i
χ1811111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111-1-11-1-1-1-1-1-111-1-11111−i−iii−i−iii−i−iiiii−i−i−i−iii−i−iii−ii−ii
χ1911111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-1111-1-11111-1-111-1-1-1-1ii−i−i−i−iii−i−iii−i−iiiii−i−iii−i−i−ii−ii
χ2011111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11-1-1111-1-11111-1-111-1-1-1-1−i−iiiii−i−iii−i−iii−i−i−i−iii−i−iiii−ii−i
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-11111-111-1-1-1-1-1-11111-1-1ii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−ii−ii
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-11111-111-1-1-1-1-1-11111-1-1−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−ii−ii−i
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-111ii−i−i−i−iii−i−iii−i−iii−i−iii−i−iiii−ii−i
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-111−i−iiiii−i−iii−i−iii−i−iii−i−iii−i−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-111111-11-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-11
χ2611111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-111-1
χ2711111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-11-1111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-111-111-1
χ2811111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-111-1-1-1-1-11-1111-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-11111-1-11-1-11
χ2911111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-1-1-11-1-1-111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-111-1
χ3011111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-1-1-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1111-1-11
χ3111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11-1-111-11-111-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11
χ3211111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11-1-111-11-111-1-111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-111-1
χ332222222222222222-2-22222-2-2-2-2222222-2-2-2-222-20000-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200002220000000000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-2-2-222-2-22222-2-2-2-222-2-220000-2-220000000000000000000000000000000000000000
χ36222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-222-2-22222-2000022-20000000000000000000000000000000000000000
χ3722222222-2-2-2-2222222-2-2-2-2222222-2-222-2-2-2-2-2-2-20000-2220000000000000000000000000000000000000000
χ3822222222-2-2-2-2222222-2-2-2-22222-2-222-2-2-2-2-2-222200002-2-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2222220000-22-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-222-2-2-200002-220000000000000000000000000000000000000000
χ4122-2-22-2-222i2i−2i−2i2i2i−2i−2i0022-2-200002-22i−2i2i−2i00002-200000000000000000000i2−i2i2−i2000000002−22−2i2−i22−22−2i2−i20000
χ4222-2-22-2-222i2i−2i−2i2i2i−2i−2i0022-2-200002-22i−2i2i−2i00002-200000000000000000000−i2i2−i2i200000000−22−22−i2i2−22−22−i2i20000
χ4322-2-22-2-222i2i−2i−2i2i2i−2i−2i0022-2-20000-22−2i2i−2i2i0000-2200000000000000000000i2−i2i2−i2000000002−22−2−i2i2−22−22−i2i20000
χ4422-2-22-2-222i2i−2i−2i2i2i−2i−2i0022-2-20000-22−2i2i−2i2i0000-2200000000000000000000−i2i2−i2i200000000−22−22i2−i22−22−2i2−i20000
χ4522-2-22-2-222i2i−2i−2i−2i−2i2i2i00-2-22200002-22i−2i−2i2i0000-22000000000000000000002−2−2200000000−i2i2i2−i22−2−i2i2i2−i2−220000
χ4622-2-22-2-222i2i−2i−2i−2i−2i2i2i00-2-22200002-22i−2i−2i2i0000-2200000000000000000000−222−200000000i2−i2−i2i2−22i2−i2−i2i22−20000
χ4722-2-22-2-222i2i−2i−2i−2i−2i2i2i00-2-2220000-22−2i2i2i−2i00002-2000000000000000000002−2−2200000000−i2i2i2−i2−22i2−i2−i2i22−20000
χ4822-2-22-2-222i2i−2i−2i−2i−2i2i2i00-2-2220000-22−2i2i2i−2i00002-200000000000000000000−222−200000000i2−i2−i2i22−2−i2i2i2−i2−220000
χ4922-2-22-2-22−2i−2i2i2i2i2i−2i−2i00-2-22200002-2−2i2i2i−2i0000-22000000000000000000002−2−2200000000i2−i2−i2i22−2i2−i2−i2i2−220000
χ5022-2-22-2-22−2i−2i2i2i2i2i−2i−2i00-2-22200002-2−2i2i2i−2i0000-2200000000000000000000−222−200000000−i2i2i2−i2−22−i2i2i2−i22−20000
χ5122-2-22-2-22−2i−2i2i2i2i2i−2i−2i00-2-2220000-222i−2i−2i2i00002-2000000000000000000002−2−2200000000i2−i2−i2i2−22−i2i2i2−i22−20000
χ5222-2-22-2-22−2i−2i2i2i2i2i−2i−2i00-2-2220000-222i−2i−2i2i00002-200000000000000000000−222−200000000−i2i2i2−i22−2i2−i2−i2i2−220000
χ5322-2-22-2-22−2i−2i2i2i−2i−2i2i2i0022-2-200002-2−2i2i−2i2i00002-200000000000000000000i2−i2i2−i200000000−22−22i2−i2−22−22i2−i20000
χ5422-2-22-2-22−2i−2i2i2i−2i−2i2i2i0022-2-200002-2−2i2i−2i2i00002-200000000000000000000−i2i2−i2i2000000002−22−2−i2i22−22−2−i2i20000
χ5522-2-22-2-22−2i−2i2i2i−2i−2i2i2i0022-2-20000-222i−2i2i−2i0000-2200000000000000000000i2−i2i2−i200000000−22−22−i2i22−22−2−i2i20000
χ5622-2-22-2-22−2i−2i2i2i−2i−2i2i2i0022-2-20000-222i−2i2i−2i0000-2200000000000000000000−i2i2−i2i2000000002−22−2i2−i2−22−22i2−i20000
χ572-22-222-2-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-20000002-22i−2i000002i−2i00000002-22-2002i−2i0000000000000000000000000000
χ582-22-222-2-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-20000002-22i−2i00000−2i2i0000000-22-2200−2i2i0000000000000000000000000000
χ592-22-222-2-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-22000000-22−2i2i0002-2000002-22i−2i00002i−2i000000000000000000000000000000
χ602-22-222-2-22-22-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-22000000-22−2i2i000-2200000-22−2i2i0000−2i2i000000000000000000000000000000
χ612-22-222-2-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-22000000-222i−2i0002-2000002-2−2i2i0000−2i2i000000000000000000000000000000
χ622-22-222-2-22-22-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-22000000-222i−2i000-2200000-222i−2i00002i−2i000000000000000000000000000000
χ632-22-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-20000002-2−2i2i000002i−2i0000000-22-22002i−2i0000000000000000000000000000
χ642-22-222-2-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-20000002-2−2i2i00000−2i2i00000002-22-200−2i2i0000000000000000000000000000
χ652-22-222-2-2-22-222i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2-2000000-22−2i2i0002-200000-22−2i2i00002i−2i000000000000000000000000000000
χ662-22-222-2-2-22-222i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2-2000000-22−2i2i000-22000002-22i−2i0000−2i2i000000000000000000000000000000
χ672-22-222-2-2-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-220000002-22i−2i000002i−2i0000000-222-200−2i2i0000000000000000000000000000
χ682-22-222-2-2-22-222i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-220000002-22i−2i00000−2i2i00000002-2-22002i−2i0000000000000000000000000000
χ692-22-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-220000002-2−2i2i000002i−2i00000002-2-2200−2i2i0000000000000000000000000000
χ702-22-222-2-2-22-22−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-220000002-2−2i2i00000−2i2i0000000-222-2002i−2i0000000000000000000000000000
χ712-22-222-2-2-22-22−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2-2000000-222i−2i0002-200000-222i−2i0000−2i2i000000000000000000000000000000
χ722-22-222-2-2-22-22−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i2-2000000-222i−2i000-22000002-2−2i2i00002i−2i000000000000000000000000000000
χ73444-4-4-44-400000000440000-4-40000000000000000000000000000000000000022−22000022−220000000000000000
χ74444-4-4-44-400000000440000-4-400000000000000000000000000000000000000−22220000−22220000000000000000
χ75444-4-4-44-400000000-4-4000044000000000000000000000000000000000000002i2−2i20000−2i22i20000000000000000
χ76444-4-4-44-400000000-4-400004400000000000000000000000000000000000000−2i22i200002i2−2i20000000000000000
χ774-444-4-4-44000000004i−4i0000−4i4i00000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ784-444-4-4-44000000004i−4i0000−4i4i0000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ794-444-4-4-4400000000−4i4i00004i−4i00000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ804-444-4-4-4400000000−4i4i00004i−4i0000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ814-4-444-44-44i−4i−4i4i4-4-4400−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-44i−4i−4i4i-444-4004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ834-4-444-44-4−4i4i4i−4i4-4-44004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ844-4-444-44-4−4i4i4i−4i-444-400−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ8588-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000

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