Finite Group Databasebeta

← Group #10772499

Character table — Group #10772499

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order12223444466644488881212121222444424444881212121212242424244448888268121212242424244444488648
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-11-11111-1-1111111111111-1-1-11-1-111-1-1-1-1-11-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-11-11111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-11-1-1-111
χ5111111111111111-1-1-1-1111111111111111-1-111111-1-1-1-1111-1-1-1-1-11-1111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-1-1-11-1-1-111-1-11-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-1-11-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1-11-1-1-1-1-1-1-111111-111-1-1-1-111111-11111-1-1
χ9111111111111-1-11111111111111111-1-1-11-1-1-1-111111111-1-11111-111-1-1-1-1-1111-1-1-11-1-1-1-11
χ10111111111111-1-1111111111111111-111-1-1-1-1-1-1-1-1111111-1-111111-1-1-111-1-1-1-1-111-1-1-1-111-1
χ11111111111111-1-1111111111-1-1-1-1-1-11-1-1-11-1-1-1-11111111-111-1-1-1-1-111-1-1-1-1-111-1111-111-11-1
χ12111111111111-1-1111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-111-1-1-1-11-1-1-111-1-1-1-11-1-111111-11
χ13111111111111-1-11-1-1-1-111111111111-1-1-1111-1-1111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-11-1-1-111111-1
χ14111111111111-1-11-1-1-1-11111111111-111-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11-1111111-111-1-111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-11-1-1-1111-1-1111-1-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-1-1111111-1-11-11111111-1-111-1-1-11-1
χ17222222-2-2222200-200002-22-22222-2-22000-20000-2-2-20000-20000000200000000-2000200000
χ18222222-2-2222200-200002-22-22222-2-2-20002000022-20000-20000000-2000000002000-200000
χ19222222-2-2222200-200002-22-2-2-2-2-2222000-20000-2-2-20000200000002000000002000-200000
χ20222222-2-2222200-200002-22-2-2-2-2-222-20002000022-2000020000000-200000000-2000200000
χ2122222-222-222222-20000-22-2222-2-2-2-2000-20002200-200002-2-20000000-20000000002000000
χ2222222-222-222222-20000-22-22-2-22222000-20002200-20000-2220000000-2000000000-2000000
χ2322222-222-2222-2-2-20000-22-2222-2-2-2-20002000-2-200-2000022200000002000000000-2000000
χ2422222-222-2222-2-2-20000-22-22-2-222220002000-2-200-20000-2-2-2000000020000000002000000
χ2522222-2-2-2-22220020000-2-2-2-222-2-22202-20000000020000-200000000002-2000002-20000000
χ2622222-2-2-2-22220020000-2-2-2-222-2-2220-220000000020000-20000000000-2200000-220000000
χ2722222-2-2-2-22220020000-2-2-2-2-2-222-2-202-20000000020000200000000002-200000-220000000
χ2822222-2-2-2-22220020000-2-2-2-2-2-222-2-20-22000000002000020000000000-22000002-20000000
χ292222-12222-1-1-12222222-1-1-1-10000002222222-1-1-1-1-1-1-1-1-100000002-12-1-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-1000000-2-2-22-222-1-111-1-1-1-1-10000000-21-2-111-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-2-2-1-1-1-1-111110000000-2-1-2-1-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-2-2-22-2-2-2-1-111-111110000000212-11111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-10000002-2-2-22-2-211-1-1-1-1-1-1-10000000-2-1211111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-222-2-2-2-21111-1-1-1-1-1000000021-21-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-10000002-2-2-222211-1-1-1111100000002-1-2111-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-222-2-2221111-111110000000-2121-1-1-1-1-1-10000000100
χ372-22-220-220-22-22i−2i0−i2−i2i2i2020-2002i−2i2i−2i000002−22i−2i000−i2−i2i2i202-222−2−20000002−20000000−i2i2000
χ382-22-220-220-22-22i−2i0−i2−i2i2i2020-200−2i2i−2i2i000002−22i−2i000−i2−i2i2i20-22−2−2220000002−20000000i2−i2000
χ392-22-220-220-22-22i−2i0i2i2−i2−i2020-2002i−2i2i−2i00000−222i−2i000i2i2−i2−i202-2−2−222000000−220000000i2−i2000
χ402-22-220-220-22-22i−2i0i2i2−i2−i2020-200−2i2i−2i2i00000−222i−2i000i2i2−i2−i20-2222−2−2000000−220000000−i2i2000
χ412-22-220-220-22-2−2i2i0−i2−i2i2i2020-2002i−2i2i−2i00000−22−2i2i000−i2−i2i2i20-2222−2−2000000−220000000i2−i2000
χ422-22-220-220-22-2−2i2i0−i2−i2i2i2020-200−2i2i−2i2i00000−22−2i2i000−i2−i2i2i202-2−2−222000000−220000000−i2i2000
χ432-22-220-220-22-2−2i2i0i2i2−i2−i2020-2002i−2i2i−2i000002−2−2i2i000i2i2−i2−i20-22−2−2220000002−20000000−i2i2000
χ442-22-220-220-22-2−2i2i0i2i2−i2−i2020-200−2i2i−2i2i000002−2−2i2i000i2i2−i2−i202-222−2−20000002−20000000i2−i2000
χ454444-24-4-44-2-2-200-40000-22-220000004000-40000222000000000000-2000000000000000000
χ464444-24-4-44-2-2-200-40000-22-22000000-400040000-2-220000000000002000000000000000000
χ474444-2-444-4-2-2-244-400002-22-2000000000-4000-2-20020000000000000020000000000000000
χ484444-2-444-4-2-2-2-4-4-400002-22-200000000040002200200000000000000-20000000000000000
χ494444-2-4-4-4-4-2-2-20040000222200000004-400000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-2004000022220000000-4400000000-20000000000000002-200000000000000
χ5144-4-44400-4-4-4400022−2222−2240-4000000000000000000022−2222−22000000000000000000000000000
χ5244-4-44400-4-4-44000−2222−222240-40000000000000000000−2222−2222000000000000000000000000000
χ5344-4-44-4004-4-440000000-40400000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5444-4-44-4004-4-440000000-404000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5544-4-4-2400-422-200022−2222−22-202000000000000000023−230−22−220000000000000006−60000000000
χ5644-4-4-2400-422-200022−2222−22-2020000000000000000−23230−22−22000000000000000−660000000000
χ5744-4-4-2400-422-2000−2222−2222-202000000000000000023−2302−22−2000000000000000−660000000000
χ5844-4-4-2400-422-2000−2222−2222-2020000000000000000−232302−22−20000000000000006−60000000000
χ594-44-4404-40-44-400000000-404004i−4i−4i4i0000000000000000000000000000000000000000000
χ604-44-4404-40-44-400000000-40400−4i4i4i−4i0000000000000000000000000000000000000000000
χ614-44-4-20-4402-224i−4i0−2i2−2i22i22i20-2020000000000022−22−2i2i000i2i2−i2−i20000000000000−22000000000000
χ624-44-4-20-4402-224i−4i02i22i2−2i2−2i20-20200000000000−2222−2i2i000−i2−i2i2i200000000000002−2000000000000
χ634-44-4-20-4402-22−4i4i0−2i2−2i22i22i20-20200000000000−22222i−2i000i2i2−i2−i200000000000002−2000000000000
χ644-44-4-20-4402-22−4i4i02i22i2−2i2−2i20-2020000000000022−222i−2i000−i2−i2i2i20000000000000−22000000000000
χ654-4-44400004-4-40002i−2i−2i2i00004-400000000000000002i−2i−2i2i0002i−2i−2i2i00000000000000000000
χ664-4-44400004-4-40002i−2i−2i2i0000-4400000000000000002i−2i−2i2i000−2i2i2i−2i00000000000000000000
χ674-4-44400004-4-4000−2i2i2i−2i00004-40000000000000000−2i2i2i−2i000−2i2i2i−2i00000000000000000000
χ684-4-44400004-4-4000−2i2i2i−2i0000-440000000000000000−2i2i2i−2i0002i−2i−2i2i00000000000000000000
χ6988-8-8-4-800844-4000000040-400000000000000000000000000000000000000000000000000
χ708-88-8-408-804-440000000040-40000000000000000000000000000000000000000000000000
χ718-8-88-40000-4440004i−4i−4i4i0000000000000000000000−2i2i2i−2i000000000000000000000000000
χ728-8-88-40000-444000−4i4i4i−4i00000000000000000000002i−2i−2i2i000000000000000000000000000

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