Finite Group Databasebeta

← Group #270205

Character table — Group #270205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222222444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-11111-1-111111111-1-1-1-11111-1-1-11-1-1-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111-1-1-11111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111111-1-111-1-111-1
χ17222222222-2-22-222-2-22222-20000-2-20000220000-2-22200000000-200000000000000
χ18222222222-2-22-222-2-22222-20000-2-20000-2-2000022-2-200000000200000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-2000022000022000022-2-200000000-200000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-20000220000-2-20000-2-22200000000200000000000000
χ2122222222-222-22-2-22-20000-2222200222200-2-2-2-2000000000000000-200000000000
χ2222222222-222-22-2-22-20000-2222200-2-2-2-20022-2-2000000000000000200000000000
χ2322222222-222-22-2-22-20000-2-2-2-2-20022-2-200-2-222000000000000000200000000000
χ2422222222-222-22-2-22-20000-2-2-2-2-200-2-222002222000000000000000-200000000000
χ252-22-2-2-222222-2-22-2-2222-2-2-200002-2000000000000000000000002i−2i00000002i−2i000
χ262-22-2-2-222222-2-22-2-2222-2-2-200002-200000000000000000000000−2i2i0000000−2i2i000
χ272-22-2-2-222222-2-22-2-22-2-222-20000-22000000000000000000000002i−2i0000000−2i2i000
χ282-22-2-2-222222-2-22-2-22-2-222-20000-2200000000000000000000000−2i2i00000002i−2i000
χ292-22-2-2-2222-2-2-222-22-222-2-220000-222-200002-20000000000000000002-2000000000
χ302-22-2-2-2222-2-2-222-22-222-2-220000-22-220000-22000000000000000000-22000000000
χ312-22-2-2-2222-2-2-222-22-2-2-222200002-22-200002-2000000000000000000-22000000000
χ322-22-2-2-2222-2-2-222-22-2-2-222200002-2-220000-220000000000000000002-2000000000
χ332-22-2-2-222-2-2-222-22220000-20000002-20000-2200000022-2-200000000002-20000000
χ342-22-2-2-222-2-2-222-22220000-20000002-20000-22000000-2-2220000000000-220000000
χ352-22-2-2-222-2-2-222-22220000-2000000-2200002-200000022-2-20000000000-220000000
χ362-22-2-2-222-2-2-222-22220000-2000000-2200002-2000000-2-22200000000002-20000000
χ372-2-22-222-220020-2-2002i−2i2i−2i022−2−20000002-2002−2002i−2ii2−i2i2−i2i2i2−i2−i20000000000002−20
χ382-2-22-222-220020-2-2002i−2i2i−2i022−2−2000000-22002−200−2i2ii2−i2i2−i2−i2−i2i2i2000000000000−220
χ392-2-22-222-220020-2-2002i−2i2i−2i0−2−2220000002-200−22002i−2i−i2i2−i2i2−i2−i2i2i2000000000000−220
χ402-2-22-222-220020-2-2002i−2i2i−2i0−2−222000000-2200−2200−2i2i−i2i2−i2i2i2i2−i2−i20000000000002−20
χ412-2-22-222-220020-2-200−2i2i−2i2i022−2−20000002-2002−200−2i2i−i2i2−i2i2−i2−i2i2i20000000000002−20
χ422-2-22-222-220020-2-200−2i2i−2i2i022−2−2000000-22002−2002i−2i−i2i2−i2i2i2i2−i2−i2000000000000−220
χ432-2-22-222-220020-2-200−2i2i−2i2i0−2−2220000002-200−2200−2i2ii2−i2i2−i2i2i2−i2−i2000000000000−220
χ442-2-22-222-220020-2-200−2i2i−2i2i0−2−222000000-2200−22002i−2ii2−i2i2−i2−i2−i2i2i20000000000002−20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ464444-4-4-4-40000000000000022−2222−2200000000000022−220000002-22-2000000000000000
χ474444-4-4-4-40000000000000022−2222−22000000000000−2222000000-22-22000000000000000
χ484444-4-4-4-400000000000000−2222−222200000000000022−22000000-22-22000000000000000
χ494444-4-4-4-400000000000000−2222−2222000000000000−22220000002-22-2000000000000000
χ5044-4-44-44-4400-40-44004i−4i−4i4i00000000000000000000000000000000000000000000
χ5144-4-44-44-4400-40-4400−4i4i4i−4i00000000000000000000000000000000000000000000
χ5244-4-44-44-4-400404-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5344-4-44-44-4-400404-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5444-4-4-44-4404-40400-40000000000000000000000000000000000000000002i2−2i200000
χ5544-4-4-44-4404-40400-4000000000000000000000000000000000000000000−2i22i200000
χ5644-4-4-44-440-440-4004000000000000004-4000000000000000000000000000000000
χ5744-4-4-44-440-440-400400000000000000-44000000000000000000000000000000000
χ584-44-4-4-444-4444-4-44-4-4000040000000000000000000000000000000000000000000
χ594-4-444-4-4404-40-40040000004-4-44000000000000000000000000000000000000000
χ604-4-444-4-4404-40-4004000000-444-4000000000000000000000000000000000000000
χ614-4-444-4-440-440400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-444-4-440-440400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-44-444-4-400-404400000002222−22−220000000000−2222000000000000000000000000000
χ644-4-44-444-4-400-40440000000−22−222222000000000022−22000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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