Finite Group Databasebeta

← Group #315021

Character table — Group #315021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888224444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-111-1
χ17222222222-222-2-2-222222222200000000-2-2-2-2-2-200000000000022-2-2-2-2000022000000000000000000000000
χ18222222222-222-2-2-222222222200000000-2-2-2-2-2-2000000000000-2-222220000-2-2000000000000000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-2-2-200000000-2-222220000000000002222-2-20000-2-2000000000000000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-2-2-200000000-2-22222000000000000-2-2-2-222000022000000000000000000000000
χ2122222222-22-2-2222-20000000022222222-2-20000-2-2-2-200000000000000222200-2-2-2-200000000000000000000
χ2222222222-22-2-2222-20000000022222222-2-20000-2-2-2-200000000000000-2-2-2-200222200000000000000000000
χ2322222222-22-2-2222-200000000-2-2-2-2-2-2-2-2-2-2000022220000000000000022-2-200-2-22200000000000000000000
χ2422222222-22-2-2222-200000000-2-2-2-2-2-2-2-2-2-20000222200000000000000-2-2220022-2-200000000000000000000
χ25222-2-2-22-2-202-200022i2i2i2i−2i−2i−2i−2i2222−2−2−2−200000022−2−2i2i2i2i2−i2−i2−i2−i22-2000000002i−2i0000i2i2−i2−i222−2−2000000000000
χ26222-2-2-22-2-202-200022i2i2i2i−2i−2i−2i−2i2222−2−2−2−200000022−2−2i2i2i2i2−i2−i2−i2−i2-2200000000−2i2i0000−i2−i2i2i2−2−222000000000000
χ27222-2-2-22-2-202-200022i2i2i2i−2i−2i−2i−2i−2−2−2−22222000000−2−222−i2−i2−i2−i2i2i2i2i22-2000000002i−2i0000−i2−i2i2i2−2−222000000000000
χ28222-2-2-22-2-202-200022i2i2i2i−2i−2i−2i−2i−2−2−2−22222000000−2−222−i2−i2−i2−i2i2i2i2i2-2200000000−2i2i0000i2i2−i2−i222−2−2000000000000
χ29222-2-2-22-2-202-20002−2i−2i−2i−2i2i2i2i2i2222−2−2−2−200000022−2−2−i2−i2−i2−i2i2i2i2i22-200000000−2i2i0000−i2−i2i2i222−2−2000000000000
χ30222-2-2-22-2-202-20002−2i−2i−2i−2i2i2i2i2i2222−2−2−2−200000022−2−2−i2−i2−i2−i2i2i2i2i2-22000000002i−2i0000i2i2−i2−i2−2−222000000000000
χ31222-2-2-22-2-202-20002−2i−2i−2i−2i2i2i2i2i−2−2−2−22222000000−2−222i2i2i2i2−i2−i2−i2−i22-200000000−2i2i0000i2i2−i2−i2−2−222000000000000
χ32222-2-2-22-2-202-20002−2i−2i−2i−2i2i2i2i2i−2−2−2−22222000000−2−222i2i2i2i2−i2−i2−i2−i2-22000000002i−2i0000−i2−i2i2i222−2−2000000000000
χ3322-22-2-2-2222-2-2-22-222i2i−2i−2i2i2i−2i−2i00000000-222i2i−2i−2i00000000000000000000000000002-22-22i−2i2i−2i000000000000
χ3422-22-2-2-2222-2-2-22-222i2i−2i−2i2i2i−2i−2i00000000-222i2i−2i−2i0000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ3522-22-2-2-2222-2-2-22-22−2i−2i2i2i−2i−2i2i2i00000000-22−2i−2i2i2i00000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ3622-22-2-2-2222-2-2-22-22−2i−2i2i2i−2i−2i2i2i00000000-22−2i−2i2i2i0000000000000000000000000000-22-222i−2i2i−2i000000000000
χ3722-22-2-2-222-2-2-22-2222i2i−2i−2i2i2i−2i−2i22-2-222-2-22-2−2i−2i2i2i2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ3822-22-2-2-222-2-2-22-2222i2i−2i−2i2i2i−2i−2i-2-222-2-2222-2−2i−2i2i2i-22-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922-22-2-2-222-2-2-22-222−2i−2i2i2i−2i−2i2i2i22-2-222-2-22-22i2i−2i−2i2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4022-22-2-2-222-2-2-22-222−2i−2i2i2i−2i−2i2i2i-2-222-2-2222-22i2i−2i−2i-22-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-22-2-2-22-2-2222-22-20000000022-2-222-2-2-220000-22-22000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ4222-22-2-2-22-2-2222-22-20000000022-2-222-2-2-220000-22-2200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ4322-22-2-2-22-2-2222-22-200000000-2-222-2-222-2200002-22-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000
χ4422-22-2-2-22-2-2222-22-200000000-2-222-2-222-2200002-22-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000
χ4522-2-222-2-2-20-22000222-2-2-2-22222−2−2−2−2220000002−2−2222−2−2−2−222002i−2i2i−2i0000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ4622-2-222-2-2-20-22000222-2-2-2-22222−2−2−2−2220000002−2−2222−2−2−2−22200−2i2i−2i2i0000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ4722-2-222-2-2-20-22000222-2-2-2-222−2−22222−2−2000000−222−2−2−22222−2−2002i−2i2i−2i0000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ4822-2-222-2-2-20-22000222-2-2-2-222−2−22222−2−2000000−222−2−2−22222−2−200−2i2i−2i2i0000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ4922-2-222-2-2-20-220002-2-22222-2-222−2−2−2−2220000002−2−22−2−22222−2−2002i−2i−2i2i0000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ5022-2-222-2-2-20-220002-2-22222-2-222−2−2−2−2220000002−2−22−2−22222−2−200−2i2i2i−2i0000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ5122-2-222-2-2-20-220002-2-22222-2-2−2−22222−2−2000000−222−222−2−2−2−222002i−2i−2i2i0000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ5222-2-222-2-2-20-220002-2-22222-2-2−2−22222−2−2000000−222−222−2−2−2−22200−2i2i2i−2i0000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ532-222-22-2-20-200-22202−22−22−22−22-22-22-22-2002−22−200002−22−22−22−20000002i−2i2i−2i00000000000000i2−i2i2−i2i2−i2i2−i20000
χ542-222-22-2-20-200-22202−22−22−22−22-22-22-22-2002−22−200002−22−22−22−2000000−2i2i−2i2i00000000000000−i2i2−i2i2−i2i2−i2i20000
χ552-222-22-2-20-200-22202−22−22−22−2-22-22-22-22002−22−20000−22−22−22−220000002i−2i−2i2i00000000000000i2−i2i2−i2−i2i2−i2i20000
χ562-222-22-2-20-200-22202−22−22−22−2-22-22-22-22002−22−20000−22−22−22−22000000−2i2i2i−2i00000000000000−i2i2−i2i2i2−i2i2−i20000
χ572-222-22-2-20-200-2220−22−22−22−222-22-22-22-200−22−220000−22−22−22−220000002i−2i2i−2i00000000000000−i2i2−i2i2−i2i2−i2i20000
χ582-222-22-2-20-200-2220−22−22−22−222-22-22-22-200−22−220000−22−22−22−22000000−2i2i−2i2i00000000000000i2−i2i2−i2i2−i2i2−i20000
χ592-222-22-2-20-200-2220−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−20000002i−2i−2i2i00000000000000−i2i2−i2i2i2−i2i2−i20000
χ602-222-22-2-20-200-2220−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−2000000−2i2i2i−2i00000000000000i2−i2i2−i2−i2i2−i2i20000
χ612-2-222-22-20200-2-220i2−i2−i2i2i2−i2−i2i22-2-222-2-2200−i2i2i2−i20000i2−i2−i2i2i2−i2−i2i20000000000002i−2i2i−2i000000002−2−222−2−220000
χ622-2-222-22-20200-2-220i2−i2−i2i2i2−i2−i2i22-2-222-2-2200−i2i2i2−i20000i2−i2−i2i2i2−i2−i2i2000000000000−2i2i−2i2i00000000−222−2−222−20000
χ632-2-222-22-20200-2-220i2−i2−i2i2i2−i2−i2i2-222-2-222-200−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i20000000000002i−2i−2i2i000000002−2−22−222−20000
χ642-2-222-22-20200-2-220i2−i2−i2i2i2−i2−i2i2-222-2-222-200−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i2000000000000−2i2i2i−2i00000000−222−22−2−220000
χ652-2-222-22-20200-2-220−i2i2i2−i2−i2i2i2−i22-2-222-2-2200i2−i2−i2i20000−i2i2i2−i2−i2i2i2−i20000000000002i−2i2i−2i00000000−222−2−222−20000
χ662-2-222-22-20200-2-220−i2i2i2−i2−i2i2i2−i22-2-222-2-2200i2−i2−i2i20000−i2i2i2−i2−i2i2i2−i2000000000000−2i2i−2i2i000000002−2−222−2−220000
χ672-2-222-22-20200-2-220−i2i2i2−i2−i2i2i2−i2-222-2-222-200i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i20000000000002i−2i−2i2i00000000−222−22−2−220000
χ682-2-222-22-20200-2-220−i2i2i2−i2−i2i2i2−i2-222-2-222-200i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i2000000000000−2i2i2i−2i000000002−2−22−222−20000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ70444-4-4-44-440-44000-40000000022222222−22−22−22−22000000−22−22222200000000000000000000000000000000000000000000
χ71444-4-4-44-440-44000-400000000−22−22−22−22222222220000002222−22−2200000000000000000000000000000000000000000000
χ7244-44-4-4-44-4444-44-4-400000000000000004-40000000000000000000000000000000000000000000000000000
χ7344-4-444-4-4404-4000-4000000002222−22−22−22−222222000000−222222−2200000000000000000000000000000000000000000000
χ7444-4-444-4-4404-4000-400000000−22−2222222222−22−2200000022−22−222200000000000000000000000000000000000000000000
χ754-444-44-4-404004-4-4022−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ764-444-44-4-404004-4-40−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000000000
χ774-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i222−2222−22−2222−222200000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ784-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2−2222−222222−2222−220000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ794-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i222−2222−22−2222−22220000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ804-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2−2222−222222−2222−2200000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ814-4-444-44-40-40044-402i2−2i2−2i22i22i2−2i2−2i22i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ824-4-444-44-40-40044-40−2i22i22i2−2i2−2i22i22i2−2i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ834-4-4-4-44440000000022−22−2222−222222−2222−22−2222−222222−2200000000002-2-22-222-2000000000000000000000000000000000000
χ844-4-4-4-44440000000022−22−2222−222222−22−222222−2222−22−22220000000000-222-22-2-22000000000000000000000000000000000000
χ854-4-4-4-444400000000−222222−2222−22−222222−22−2222−222222−220000000000-222-22-2-22000000000000000000000000000000000000
χ864-4-4-4-444400000000−222222−2222−22−2222−222222−2222−22−222200000000002-2-22-222-2000000000000000000000000000000000000

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