Finite Group Databasebeta

← Group #10772464

Character table — Group #10772464

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order12223444466644488881212121222444422444881212121212242424244448888466812122424242424444881248
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1111111111111-11-1-1-1-111-1-1-1-1-11-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-11-1-1-1-11111-1-111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111-11-1-1-111
χ5111111111111111-1-1-1-1111111111111111-1-111111-1-1-1-1111-1-1-1-1-111-111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-1111-1-1-1-111-11-1-1-1-111-1-1-11-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-11111-111-111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1111111-11-1-1-1-111111-11111-1-1
χ9111111111111-1-1111111111111111-11-1-11-1-1-1-111111111-1-11111-1-111-1-1-1-1111-1-1-11-1-1-1-11
χ10111111111111-1-1111111111111111-1-111-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-111-1-1-1-111-1
χ11111111111111-1-1111111111-1-1-1-1-1-1-11-1-11-1-1-1-11111111-111-1-1-1-1-1-111-1-1-1-111-1111-111-11-1
χ12111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-111-1-1-1-11-1-1-111-1-1-1-11-1-111111-11
χ13111111111111-1-11-1-1-1-11111111111-11-1-1111-1-1111-1-1-1-11-1-1-1-1-1-11-11-1-1-111-1-11-1-1-111111-1
χ14111111111111-1-11-1-1-1-11111111111-1-111-111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-11111111-111-1-111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-11-1-1111-1-1111-1-1-1-1-11111111-11-1-1-111-1-1-1111-1-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11-1-1-1-1-1111111-1-1-111111111-1-111-1-1-11-1
χ17222222-2-2222222-20000-22-2222-2-222-20000002200-20000-22200000-200000000000-2000000
χ18222222-2-2222222-20000-22-22-2-222-2-2-20000002200-200002-2-200000-2000000000002000000
χ19222222-2-22222-2-2-20000-22-2222-2-2222000000-2-200-20000-2-2-2000002000000000002000000
χ20222222-2-22222-2-2-20000-22-22-2-222-2-22000000-2-200-2000022200000200000000000-2000000
χ2122222-222-222200-200002-22-222-2-2-2-20200-20000-2-2-2000020000000020000000-2000200000
χ2222222-222-222200-200002-22-222-2-2-2-20-2002000022-20000200000000-200000002000-200000
χ2322222-222-222200-200002-22-2-2-222220200-20000-2-2-20000-200000000200000002000-200000
χ2422222-222-222200-200002-22-2-2-222220-2002000022-20000-200000000-20000000-2000200000
χ2522222-2-2-2-22220020000-2-2-2-22222-2-2002-2000000020000-200000000002-2000002-20000000
χ2622222-2-2-2-22220020000-2-2-2-22222-2-200-22000000020000-20000000000-2200000-220000000
χ2722222-2-2-2-22220020000-2-2-2-2-2-2-2-222002-2000000020000200000000002-200000-220000000
χ2822222-2-2-2-22220020000-2-2-2-2-2-2-2-22200-2200000002000020000000000-22000002-20000000
χ292222-12222-1-1-12222222-1-1-1-10000002222222-1-1-1-1-1-1-1-1-100000002-1-12-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-10000002-2-2-2-222-1-111-1-1-1-1-10000000-2-11-211-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-2-2-1-1-1-1-111110000000-2-1-1-2-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-10000002-2-2-2-2-2-2-1-111-1111100000002-1121111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-1000000-22-2-22-2-211-1-1-1-1-1-1-10000000-21-121111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-222-2-2-21111-1-1-1-1-10000000211-2-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-22-2-222211-1-1-11111000000021-1-211-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-222-2221111-111110000000-2112-1-1-1-1-1-10000000100
χ372-2-222200-2-2-222i−2i0−i2−i2i2i2020-22-2002-2000002−22i−2i000−i2−i2i2i202i−2i−i2−i2i2i20000002−200000002−2000
χ382-2-222200-2-2-222i−2i0−i2−i2i2i2020-2-2200-22000002−22i−2i000−i2−i2i2i20−2i2ii2i2−i2−i20000002−20000000−22000
χ392-2-222200-2-2-222i−2i0i2i2−i2−i2020-22-2002-200000−222i−2i000i2i2−i2−i202i−2ii2i2−i2−i2000000−220000000−22000
χ402-2-222200-2-2-222i−2i0i2i2−i2−i2020-2-2200-2200000−222i−2i000i2i2−i2−i20−2i2i−i2−i2i2i2000000−2200000002−2000
χ412-2-222200-2-2-22−2i2i0−i2−i2i2i2020-22-2002-200000−22−2i2i000−i2−i2i2i20−2i2i−i2−i2i2i2000000−220000000−22000
χ422-2-222200-2-2-22−2i2i0−i2−i2i2i2020-2-2200-2200000−22−2i2i000−i2−i2i2i202i−2ii2i2−i2−i2000000−2200000002−2000
χ432-2-222200-2-2-22−2i2i0i2i2−i2−i2020-22-2002-2000002−2−2i2i000i2i2−i2−i20−2i2ii2i2−i2−i20000002−200000002−2000
χ442-2-222200-2-2-22−2i2i0i2i2−i2−i2020-2-2200-22000002−2−2i2i000i2i2−i2−i202i−2i−i2−i2i2i20000002−20000000−22000
χ454444-24-4-44-2-2-244-400002-22-2000000-4000000-2-20020000000000002000000000000000000
χ464444-24-4-44-2-2-2-4-4-400002-22-2000000400000022002000000000000-2000000000000000000
χ474444-2-444-4-2-2-200-40000-22-220000000400-400002220000000000000-200000000000000000
χ484444-2-444-4-2-2-200-40000-22-220000000-40040000-2-220000000000000200000000000000000
χ494444-2-4-4-4-4-2-2-200400002222000000004-40000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-20040000222200000000-440000000-20000000000000002-200000000000000
χ5144-4-4404-404-4-400022−2222−22-404000000000000000000022−2222−22000000000000000000000000000
χ5244-4-4404-404-4-4000−2222−2222-4040000000000000000000−2222−2222000000000000000000000000000
χ5344-4-440-4404-4-4000000040-40000000000000000000000000022−2222−2200000000000000000000
χ5444-4-440-4404-4-4000000040-400000000000000000000000000−2222−222200000000000000000000
χ5544-4-4-204-40-22200022−2222−2220-2000000000000000023−230−22−220000000000000006−60000000000
χ5644-4-4-204-40-22200022−2222−2220-20000000000000000−23230−22−22000000000000000−660000000000
χ5744-4-4-204-40-222000−2222−222220-2000000000000000023−2302−22−2000000000000000−660000000000
χ5844-4-4-204-40-222000−2222−222220-20000000000000000−232302−22−20000000000000006−60000000000
χ594-44-440000-44-40002i−2i−2i2i0000004-4000000000000002i−2i−2i2i0002i−2i−2i2i00000000000000000000
χ604-44-440000-44-40002i−2i−2i2i000000-44000000000000002i−2i−2i2i000−2i2i2i−2i00000000000000000000
χ614-44-440000-44-4000−2i2i2i−2i0000004-400000000000000−2i2i2i−2i000−2i2i2i−2i00000000000000000000
χ624-44-440000-44-4000−2i2i2i−2i000000-4400000000000000−2i2i2i−2i0002i−2i−2i2i00000000000000000000
χ634-4-444-4004-4-4400000000-4044-400-440000000000000000000000000000000000000000000
χ644-4-444-4004-4-4400000000-404-44004-40000000000000000000000000000000000000000000
χ654-4-44-2400-422-24i−4i0−2i2−2i22i22i20-2020000000000022−22−2i2i000i2i2−i2−i20000000000000−22000000000000
χ664-4-44-2400-422-24i−4i02i22i2−2i2−2i20-20200000000000−2222−2i2i000−i2−i2i2i200000000000002−2000000000000
χ674-4-44-2400-422-2−4i4i0−2i2−2i22i22i20-20200000000000−22222i−2i000i2i2−i2−i200000000000002−2000000000000
χ684-4-44-2400-422-2−4i4i02i22i2−2i2−2i20-2020000000000022−222i−2i000−i2−i2i2i20000000000000−22000000000000
χ6988-8-8-40-880-4440000000-40400000000000000000000000000000000000000000000000000
χ708-88-8-400004-440004i−4i−4i4i0000000000000000000000−2i2i2i−2i000000000000000000000000000
χ718-88-8-400004-44000−4i4i4i−4i00000000000000000000002i−2i−2i2i000000000000000000000000000
χ728-8-88-4-800844-40000000040-40000000000000000000000000000000000000000000000000

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