Finite Group Databasebeta

← Group #288752

Character table — Group #288752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888222244444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ7111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-11-11
χ91111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-111-1
χ17222222222-2-22-222-22222222200000000-2-20000-2-2-2-20000000022-2-20000-2-222000000000000000000000000
χ18222222222-2-22-222-22222222200000000-2-20000-2-2-2-200000000-2-222000022-2-2000000000000000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-2-2-200000000-2-2000022220000000022220000-2-2-2-2000000000000000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-200000000-2-20000222200000000-2-2-2-200002222000000000000000000000000
χ2122222222-222-22-2-220000000022222222-2-2-2-2-2-2000000000000000022-2-2000022-2-200000000000000000000
χ2222222222-222-22-2-220000000022222222-2-2-2-2-2-20000000000000000-2-2220000-2-22200000000000000000000
χ2322222222-222-22-2-2200000000-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-20000-2-22200000000000000000000
χ2422222222-222-22-2-2200000000-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222000022-2-200000000000000000000
χ25222-2-2-22-202-20-20022222−2−2−2−22222-2-2-2-200000022−2−22222−2−2−2−20000002i−2i0000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ26222-2-2-22-202-20-20022222−2−2−2−22222-2-2-2-200000022−2−22222−2−2−2−2000000−2i2i000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ27222-2-2-22-202-20-20022222−2−2−2−2-2-2-2-2222200000022−2−2−2−2−2−222220000002i−2i000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ28222-2-2-22-202-20-20022222−2−2−2−2-2-2-2-2222200000022−2−2−2−2−2−22222000000−2i2i0000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ29222-2-2-22-202-20-2002−2−2−2−222222222-2-2-2-2000000−2−222−2−2−2−222220000002i−2i0000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ30222-2-2-22-202-20-2002−2−2−2−222222222-2-2-2-2000000−2−222−2−2−2−22222000000−2i2i000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ31222-2-2-22-202-20-2002−2−2−2−22222-2-2-2-22222000000−2−2222222−2−2−2−20000002i−2i000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ32222-2-2-22-202-20-2002−2−2−2−22222-2-2-2-22222000000−2−2222222−2−2−2−2000000−2i2i0000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ3322-222-2-2-2-200-202202i2i−2i−2i2i2i−2i−2i22−2−222−2−20022−2−20000i2i2−i2−i2i2i2−i2−i2002-200002i−2i00000000000000i2i2−i2−i222−2−20000
χ3422-222-2-2-2-200-202202i2i−2i−2i2i2i−2i−2i22−2−222−2−20022−2−20000i2i2−i2−i2i2i2−i2−i200-220000−2i2i00000000000000−i2−i2i2i2−2−2220000
χ3522-222-2-2-2-200-202202i2i−2i−2i2i2i−2i−2i−2−222−2−22200−2−2220000−i2−i2i2i2−i2−i2i2i2002-200002i−2i00000000000000−i2−i2i2i2−2−2220000
χ3622-222-2-2-2-200-202202i2i−2i−2i2i2i−2i−2i−2−222−2−22200−2−2220000−i2−i2i2i2−i2−i2i2i200-220000−2i2i00000000000000i2i2−i2−i222−2−20000
χ3722-222-2-2-2-200-20220−2i−2i2i2i−2i−2i2i2i22−2−222−2−20022−2−20000−i2−i2i2i2−i2−i2i2i2002-20000−2i2i00000000000000−i2−i2i2i222−2−20000
χ3822-222-2-2-2-200-20220−2i−2i2i2i−2i−2i2i2i22−2−222−2−20022−2−20000−i2−i2i2i2−i2−i2i2i200-2200002i−2i00000000000000i2i2−i2−i2−2−2220000
χ3922-222-2-2-2-200-20220−2i−2i2i2i−2i−2i2i2i−2−222−2−22200−2−2220000i2i2−i2−i2i2i2−i2−i2002-20000−2i2i00000000000000i2i2−i2−i2−2−2220000
χ4022-222-2-2-2-200-20220−2i−2i2i2i−2i−2i2i2i−2−222−2−22200−2−2220000i2i2−i2−i2i2i2−i2−i200-2200002i−2i00000000000000−i2−i2i2i222−2−20000
χ412-22-222-2-2200-20-2202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i200i2−i2i2−i200002−22−22−22−22-2000000002i−2i000000000000i2−i2i2−i22−22−20000
χ422-22-222-2-2200-20-2202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i200i2−i2i2−i200002−22−22−22−2-2200000000−2i2i000000000000−i2i2−i2i2−22−220000
χ432-22-222-2-2200-20-2202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−i2i2−i2i20000−22−22−22−222-2000000002i−2i000000000000−i2i2−i2i2−22−220000
χ442-22-222-2-2200-20-2202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−i2i2−i2i20000−22−22−22−22-2200000000−2i2i000000000000i2−i2i2−i22−22−20000
χ452-22-222-2-2200-20-220−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200i2−i2i2−i20000−22−22−22−222-200000000−2i2i000000000000i2−i2i2−i2−22−220000
χ462-22-222-2-2200-20-220−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200i2−i2i2−i20000−22−22−22−22-22000000002i−2i000000000000−i2i2−i2i22−22−20000
χ472-22-222-2-2200-20-220−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200−i2i2−i2i200002−22−22−22−22-200000000−2i2i000000000000−i2i2−i2i22−22−20000
χ482-22-222-2-2200-20-220−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200−i2i2−i2i200002−22−22−22−2-22000000002i−2i000000000000i2−i2i2−i2−22−220000
χ492-2-22-222-202-20200-22−2−22−222−22i−2i−2i2i−2i2i2i−2i0000002−22−2−i2i2i2−i2i2−i2−i2i200002i−2i0000002-200i2−i2i2−i22−22−2000000000000
χ502-2-22-222-202-20200-22−2−22−222−22i−2i−2i2i−2i2i2i−2i0000002−22−2−i2i2i2−i2i2−i2−i2i20000−2i2i000000-2200−i2i2−i2i2−22−22000000000000
χ512-2-22-222-202-20200-22−2−22−222−2−2i2i2i−2i2i−2i−2i2i0000002−22−2i2−i2−i2i2−i2i2i2−i200002i−2i000000-2200i2−i2i2−i2−22−22000000000000
χ522-2-22-222-202-20200-22−2−22−222−2−2i2i2i−2i2i−2i−2i2i0000002−22−2i2−i2−i2i2−i2i2i2−i20000−2i2i0000002-200−i2i2−i2i22−22−2000000000000
χ532-2-22-222-202-20200-2−222−22−2−222i−2i−2i2i−2i2i2i−2i000000−22−22i2−i2−i2i2−i2i2i2−i200002i−2i0000002-200−i2i2−i2i2−22−22000000000000
χ542-2-22-222-202-20200-2−222−22−2−222i−2i−2i2i−2i2i2i−2i000000−22−22i2−i2−i2i2−i2i2i2−i20000−2i2i000000-2200i2−i2i2−i22−22−2000000000000
χ552-2-22-222-202-20200-2−222−22−2−22−2i2i2i−2i2i−2i−2i2i000000−22−22−i2i2i2−i2i2−i2−i2i200002i−2i000000-2200−i2i2−i2i22−22−2000000000000
χ562-2-22-222-202-20200-2−222−22−2−22−2i2i2i−2i2i−2i−2i2i000000−22−22−i2i2i2−i2i2−i2−i2i20000−2i2i0000002-200i2−i2i2−i2−22−22000000000000
χ572-2-2-22-222222-2-22-2-2000000002i−2i−2i2i2i−2i−2i2i-22−2i2i2i−2i00000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ582-2-2-22-222222-2-22-2-2000000002i−2i−2i2i2i−2i−2i2i-22−2i2i2i−2i0000000000000000000000000000-222-22i−2i−2i2i000000000000
χ592-2-2-22-222222-2-22-2-200000000−2i2i2i−2i−2i2i2i−2i-222i−2i−2i2i00000000000000000000000000002-2-222i−2i−2i2i000000000000
χ602-2-2-22-222222-2-22-2-200000000−2i2i2i−2i−2i2i2i−2i-222i−2i−2i2i0000000000000000000000000000-222-2−2i2i2i−2i000000000000
χ612-2-2-22-222-2222-2-22-22-2-222-2-222i−2i−2i2i2i−2i−2i2i2-22i−2i−2i2i2-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ622-2-2-22-222-2222-2-22-22-2-222-2-22−2i2i2i−2i−2i2i2i−2i2-2−2i2i2i−2i2-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ632-2-2-22-222-2222-2-22-2-222-2-222-22i−2i−2i2i2i−2i−2i2i2-22i−2i−2i2i-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ642-2-2-22-222-2222-2-22-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i2-2−2i2i2i−2i-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ652-2-2-22-222-2-2-222-2222-2-222-2-2200000000-220000-222-2000000000000000000000000000000002-2-222-2-220000
χ662-2-2-22-222-2-2-222-2222-2-222-2-2200000000-220000-222-200000000000000000000000000000000-222-2-222-20000
χ672-2-2-22-222-2-2-222-222-222-2-222-200000000-2200002-2-22000000000000000000000000000000002-2-22-222-20000
χ682-2-2-22-222-2-2-222-222-222-2-222-200000000-2200002-2-2200000000000000000000000000000000-222-22-2-220000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ70444-4-4-44-40-440400-422222222−22−22−22−2200000000000000−22−22222200000000000000000000000000000000000000000000
χ71444-4-4-44-40-440400-4−22−22−22−2222222222000000000000002222−22−2200000000000000000000000000000000000000000000
χ7244-444-4-4-440040-4-40000000002222−22−222222−22−2200−22−222222000000000000000000000000000000000000000000000000
χ7344-444-4-4-440040-4-4000000000−22−222222−22−222222002222−22−22000000000000000000000000000000000000000000000000
χ7444-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i22222−22−22−22−22222200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ7544-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i2−22−2222222222−22−220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7644-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i22222−22−22−22−2222220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7744-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i2−22−2222222222−22−2200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ784-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i200000000002-22-2-22-22000000000000000000000000000000000000
χ794-444-4-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000-22-222-22-2000000000000000000000000000000000000
χ804-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000-22-222-22-2000000000000000000000000000000000000
χ814-444-4-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i200000000002-22-2-22-22000000000000000000000000000000000000
χ824-44-444-4-4-400404-40000000002i2−2i22i2−2i22i2−2i22i2−2i200−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ834-44-444-4-4-400404-4000000000−2i22i2−2i22i2−2i22i2−2i22i2002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ844-4-44-444-40-440-400422−22−2222−222222−2200000000000000−2222−222200000000000000000000000000000000000000000000
χ854-4-44-444-40-440-4004−222222−2222−22−22220000000000000022−2222−2200000000000000000000000000000000000000000000
χ864-4-4-44-4444-4-4-444-4400000000000000004-40000000000000000000000000000000000000000000000000000

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