Finite Group Databasebeta

← Group #120576

Character table — Group #120576

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i−i−iii
χ172222222222222222222222-2-2-2-2-2-22-2-22-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ182222222222222222222222-2-2-2-2-2-22-2-22-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2222222-222-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2222222-222-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-222-222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-222-222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ292222-2-2-2-22222-2-2-2-222-2-22-2000000200-2000022-2-222-2-2000000000000000022−2−222−2−222−2−222−2−20000000000000000
χ302222-2-2-2-22222-2-2-2-222-2-22-2000000200-2000022-2-222-2-20000000000000000−2−222−2−222−2−222−2−2220000000000000000
χ312222-2-2-2-22222-2-2-2-222-2-22-2000000200-20000-2-222-2-222000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ322222-2-2-2-22222-2-2-2-222-2-22-2000000200-20000-2-222-2-2220000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ332222-2-2-2-2-2-2-2-22222-2-2222-2000000200-2000022-2-2-2-2220000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-2-2-22222-2-2222-2000000200-2000022-2-2-2-2220000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-2-2-22222-2-2222-2000000200-20000-2-22222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-2-2-22222-2-2222-2000000200-20000-2-22222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ3722-2-22-22-22i2i−2i−2i2i2i−2i−2i00000022-2-22i−2i02i−2i00000i2−i2i2−i22−22−2i2i2−i2−i222−2−2002i−2i002-200000000000000002−22−2i2−i2i2−i200000000
χ3822-2-22-22-22i2i−2i−2i2i2i−2i−2i00000022-2-22i−2i02i−2i00000i2−i2i2−i22−22−2i2i2−i2−i222−2−200−2i2i00-220000000000000000−22−22−i2i2−i2i200000000
χ3922-2-22-22-22i2i−2i−2i2i2i−2i−2i00000022-2-22i−2i02i−2i00000−i2i2−i2i2−22−22−i2−i2i2i2−2−222002i−2i002-20000000000000000−22−22−i2i2−i2i200000000
χ4022-2-22-22-22i2i−2i−2i2i2i−2i−2i00000022-2-22i−2i02i−2i00000−i2i2−i2i2−22−22−i2−i2i2i2−2−22200−2i2i00-2200000000000000002−22−2i2−i2i2−i200000000
χ4122-2-22-22-22i2i−2i−2i2i2i−2i−2i000000-2-222−2i2i0−2i2i00000i2−i2i2−i22−22−2−i2−i2i2i2−2−2222-2002i−2i000000000000000000i2−i2−i2i2−222−200000000
χ4222-2-22-22-22i2i−2i−2i2i2i−2i−2i000000-2-222−2i2i0−2i2i00000i2−i2i2−i22−22−2−i2−i2i2i2−2−222-2200−2i2i000000000000000000−i2i2i2−i22−2−2200000000
χ4322-2-22-22-22i2i−2i−2i2i2i−2i−2i000000-2-222−2i2i0−2i2i00000−i2i2−i2i2−22−22i2i2−i2−i222−2−22-2002i−2i000000000000000000−i2i2i2−i22−2−2200000000
χ4422-2-22-22-22i2i−2i−2i2i2i−2i−2i000000-2-222−2i2i0−2i2i00000−i2i2−i2i2−22−22i2i2−i2−i222−2−2-2200−2i2i000000000000000000i2−i2−i2i2−222−200000000
χ4522-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000022-2-2−2i2i0−2i2i00000i2−i2i2−i2−22−22i2i2−i2−i2−2−222002i−2i00-2200000000000000002−22−2−i2i2−i2i200000000
χ4622-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000022-2-2−2i2i0−2i2i00000i2−i2i2−i2−22−22i2i2−i2−i2−2−22200−2i2i002-20000000000000000−22−22i2−i2i2−i200000000
χ4722-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000022-2-2−2i2i0−2i2i00000−i2i2−i2i22−22−2−i2−i2i2i222−2−2002i−2i00-220000000000000000−22−22i2−i2i2−i200000000
χ4822-2-22-22-2−2i−2i2i2i−2i−2i2i2i00000022-2-2−2i2i0−2i2i00000−i2i2−i2i22−22−2−i2−i2i2i222−2−200−2i2i002-200000000000000002−22−2−i2i2−i2i200000000
χ4922-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000-2-2222i−2i02i−2i00000i2−i2i2−i2−22−22−i2−i2i2i222−2−22-200−2i2i000000000000000000i2−i2−i2i22−2−2200000000
χ5022-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000-2-2222i−2i02i−2i00000i2−i2i2−i2−22−22−i2−i2i2i222−2−2-22002i−2i000000000000000000−i2i2i2−i2−222−200000000
χ5122-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000-2-2222i−2i02i−2i00000−i2i2−i2i22−22−2i2i2−i2−i2−2−2222-200−2i2i000000000000000000−i2i2i2−i2−222−200000000
χ5222-2-22-22-2−2i−2i2i2i−2i−2i2i2i000000-2-2222i−2i02i−2i00000−i2i2−i2i22−22−2i2i2−i2−i2−2−222-22002i−2i000000000000000000i2−i2−i2i22−2−2200000000
χ532-2-2222-2-22-22-22-22-22-22-2222-22-222-2-2-2-22-22-200000000000000000000000000000000000000000000000000002-22-2
χ542-2-2222-2-22-22-22-22-22-22-2222-22-222-2-2-2-22-22-20000000000000000000000000000000000000000000000000000-22-22
χ552-2-2222-2-22-22-22-22-22-22-222-22-22-2-2-222-2-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ562-2-2222-2-22-22-22-22-22-22-222-22-22-2-2-222-2-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ572-2-2222-2-22-22-22-22-2-22-22-2-22-22-2222-2-22-22-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ582-2-2222-2-22-22-22-22-2-22-22-2-22-22-2222-2-22-22-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ592-2-2222-2-22-22-22-22-2-22-22-2-2-22-22-2-222222-22-20000000000000000000000002-22-22-22-2000000000000000000000000
χ602-2-2222-2-22-22-22-22-2-22-22-2-2-22-22-2-222222-22-2000000000000000000000000-22-22-22-22000000000000000000000000
χ612-2-2222-2-2-22-22-22-222-22-2-2-22-22-2-2-22222-222-2000000000000000000000000000000002-22-2-22-220000000000000000
χ622-2-2222-2-2-22-22-22-222-22-2-2-22-22-2-2-22222-222-200000000000000000000000000000000-22-222-22-20000000000000000
χ632-2-2222-2-2-22-22-22-222-22-2-2-2-22-22222-2-222-2-220000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ642-2-2222-2-2-22-22-22-222-22-2-2-2-22-22222-2-222-2-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ652-2-2222-2-2-22-22-22-22-22-22222-22-2-2-2-222-22-2-2200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ662-2-2222-2-2-22-22-22-22-22-22222-22-2-2-2-222-22-2-220000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ672-2-2222-2-2-22-22-22-22-22-2222-22-2222-2-2-2-2-222-20000000000000000000000000000000000000000000000002-2-220000
χ682-2-2222-2-2-22-22-22-22-22-2222-22-2222-2-2-2-2-222-2000000000000000000000000000000000000000000000000-222-20000
χ692-2-22-2-2222-22-2-22-22-222-2-22000000200-20000000000002i−2i2i−2i2i−2i2i−2i000000002−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ702-2-22-2-2222-22-2-22-22-222-2-22000000200-20000000000002i−2i2i−2i2i−2i2i−2i00000000−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ712-2-22-2-2222-22-2-22-22-222-2-22000000200-2000000000000−2i2i−2i2i−2i2i−2i2i000000002−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ722-2-22-2-2222-22-2-22-22-222-2-22000000200-2000000000000−2i2i−2i2i−2i2i−2i2i00000000−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ732-2-22-2-222-22-222-22-22-2-22-22000000200-20000000000002i−2i2i−2i−2i2i−2i2i00000000i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ742-2-22-2-222-22-222-22-22-2-22-22000000200-20000000000002i−2i2i−2i−2i2i−2i2i00000000−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ752-2-22-2-222-22-222-22-22-2-22-22000000200-2000000000000−2i2i−2i2i2i−2i2i−2i00000000i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ762-2-22-2-222-22-222-22-22-2-22-22000000200-2000000000000−2i2i−2i2i2i−2i2i−2i00000000−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ774444-4-4-4-44444-4-4-4-4-4-444-44000000-4004000000000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-4-4-4-4-4444444-4-4-44000000-4004000000000000000000000000000000000000000000000000000000000000
χ7944-4-4-44-444i4i−4i−4i−4i−4i4i4i000000000000000000002i2−2i2−2i22i222−22−2222000000000000000000000000000000000000000000000000
χ8044-4-4-44-444i4i−4i−4i−4i−4i4i4i00000000000000000000−2i22i22i2−2i2−222222−22000000000000000000000000000000000000000000000000
χ8144-4-4-44-44−4i−4i4i4i4i4i−4i−4i000000000000000000002i2−2i2−2i22i2−222222−22000000000000000000000000000000000000000000000000
χ8244-4-4-44-44−4i−4i4i4i4i4i−4i−4i00000000000000000000−2i22i22i2−2i222−22−2222000000000000000000000000000000000000000000000000
χ834-44-44-4-444i−4i−4i4i4i−4i−4i4i0000004-4-444i−4i0−4i4i0000000000000000000000000000000000000000000000000000000000000
χ844-44-44-4-444i−4i−4i4i4i−4i−4i4i000000-444-4−4i4i04i−4i0000000000000000000000000000000000000000000000000000000000000
χ854-44-44-4-44−4i4i4i−4i−4i4i4i−4i0000004-4-44−4i4i04i−4i0000000000000000000000000000000000000000000000000000000000000
χ864-44-44-4-44−4i4i4i−4i−4i4i4i−4i000000-444-44i−4i0−4i4i0000000000000000000000000000000000000000000000000000000000000
χ874-44-4-444-44i−4i−4i4i−4i4i4i−4i000000000000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ884-44-4-444-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ894-44-4-444-4−4i4i4i−4i4i−4i−4i4i000000000000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ904-44-4-444-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ914-4-44-4-4444-44-4-44-444-4-444-4000000-4004000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-444-44-4-444-44-4000000-4004000000000000000000000000000000000000000000000000000000000000

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