Finite Group Databasebeta

← Group #10772501

Character table — Group #10772501

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order122234444666444888812121212224444444448812121212122424242444488882812121212242424242444488648
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-11-11111-1-1111111111111-1-11-1-1-111-1-1-11-1-1-111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-11-11111-1-111111-1-1-1-1-1-1-1-1-11-1-1-111-1-11-1111-1-1-111
χ5111111111111111-1-1-1-1111111111111111-1-111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1
χ6111111111111111-1-1-1-11111111111-1-1-11-1-1-111-1-11-1-1-1-1111-1-1-1-1111-1-1-1-1-111-11-1-1-1-1-1111
χ7111111111111111-1-1-1-11111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-111-111
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1-11-1-1-1-1-1-1-11111111-1-1-1-1-1111-1111111-1-1
χ9111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111111-1-1111111-1-111-1-1-1-1-1-1-111-1-1-111-1
χ10111111111111-1-1111111111111111-1-11-11-1-1-1-11111111-1-111111-11-1-1-11-1-1111-1-1-11-1-1-1-11
χ11111111111111-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11-1-111-1-1-1-1-111-1-11111-11
χ12111111111111-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-1-1111111111-1-1-1-1-1-11-1-1-11-1-111-1111-111-11-1
χ13111111111111-1-11-1-1-1-1111111111111-1-1-111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11-111-11111-1-111-111-1-11
χ14111111111111-1-11-1-1-1-11111111111-1-11-1111-1-1111-1-1-1-1-1-11-1-1-1-11-1-1-1-1111-1-11-1-1-111111-1
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-11-1-1-1-111-11111-11-111-1111111-1-11-1-1-11-1
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-1111-1-1-1-111-111111-1-1-1-1111-1-1-1111-1-1-11-11
χ17222222-2-2222200-20000-22-222222-2-20020-20000-2-2-2000000-200000000020000-2000200000
χ18222222-2-2222200-20000-22-222222-2-200-202000022-2000000-2000000000-200002000-200000
χ19222222-2-2222200-20000-22-22-2-2-2-2220020-20000-2-2-20000002000000000200002000-200000
χ20222222-2-2222200-20000-22-22-2-2-2-22200-202000022-20000002000000000-20000-2000200000
χ2122222-222-222222-200002-22-222-2-2-2-2000-20002200-20000-2-22000000-200000000200000000
χ2222222-222-222222-200002-22-2-2-22222000-20002200-2000022-2000000-200000000-200000000
χ2322222-222-2222-2-2-200002-22-222-2-2-2-20002000-2-200-20000222000000200000000-200000000
χ2422222-222-2222-2-2-200002-22-2-2-222220002000-2-200-20000-2-2-2000000200000000200000000
χ2522222-2-2-2-22220020000-2-2-2-222-2-2222-20000000002000000-200000002-200000002-2000000
χ2622222-2-2-2-22220020000-2-2-2-222-2-222-220000000002000000-20000000-220000000-22000000
χ2722222-2-2-2-22220020000-2-2-2-2-2-222-2-22-20000000002000000200000002-20000000-22000000
χ2822222-2-2-2-22220020000-2-2-2-2-2-222-2-2-22000000000200000020000000-2200000002-2000000
χ292222-12222-1-1-12222222-1-1-1-10000002222222-1-1-1-1-1-1-1-1-1000000022-1-1-1-1-1-1-1-10000000-100
χ302222-12222-1-1-12222222-1-1-1-1000000-2-2-22-222-1-111-1-1-1-1-10000000-2-2-1111-1-1110000000100
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-100000022222-2-2-1-1-1-1-111110000000-2-2-1-1-1-111110000000100
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-2-2-22-2-2-2-1-111-11111000000022-111111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-100000022-2-2-2-2-21111-1-1-1-1-100000002-21-1-1111110000000-100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-22-22-2-211-1-1-1-1-1-1-10000000-22111-111-1-10000000100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-100000022-2-2-2221111-111110000000-221-1-11-1-1-1-10000000100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-22-222211-1-1-1111100000002-2111-1-1-1110000000-100
χ372-2-22202-202-2-22-20−i2−i2i2i2-2020002i−2i2i−2i00000−i2i22-2000−i2−i2i2i22i−2i022−2−2000000−i2i200000002−2000
χ382-2-22202-202-2-22-20−i2−i2i2i2-202000−2i2i−2i2i00000−i2i22-2000−i2−i2i2i2−2i2i0−2−222000000−i2i20000000−22000
χ392-2-22202-202-2-22-20i2i2−i2−i2-2020002i−2i2i−2i00000i2−i22-2000i2i2−i2−i22i−2i0−2−222000000i2−i20000000−22000
χ402-2-22202-202-2-22-20i2i2−i2−i2-202000−2i2i−2i2i00000i2−i22-2000i2i2−i2−i2−2i2i022−2−2000000i2−i200000002−2000
χ412-2-22202-202-2-2-220−i2−i2i2i2-2020002i−2i2i−2i00000i2−i2-22000−i2−i2i2i2−2i2i022−2−2000000i2−i20000000−22000
χ422-2-22202-202-2-2-220−i2−i2i2i2-202000−2i2i−2i2i00000i2−i2-22000−i2−i2i2i22i−2i0−2−222000000i2−i200000002−2000
χ432-2-22202-202-2-2-220i2i2−i2−i2-2020002i−2i2i−2i00000−i2i2-22000i2i2−i2−i2−2i2i0−2−222000000−i2i200000002−2000
χ442-2-22202-202-2-2-220i2i2−i2−i2-202000−2i2i−2i2i00000−i2i2-22000i2i2−i2−i22i−2i022−2−2000000−i2i20000000−22000
χ454444-24-4-44-2-2-200-400002-22-20000000040-400002220000000000000000-200000000000000
χ464444-24-4-44-2-2-200-400002-22-200000000-4040000-2-220000000000000000200000000000000
χ474444-2-444-4-2-2-244-40000-22-22000000000-4000-2-20020000000000000200000000000000000
χ484444-2-444-4-2-2-2-4-4-40000-22-220000000004000220020000000000000-200000000000000000
χ494444-2-4-4-4-4-2-2-2004000022220000004-4000000000-200000000000000-22000000000000000
χ504444-2-4-4-4-4-2-2-200400002222000000-44000000000-2000000000000002-2000000000000000
χ5144-4-44400-4-4-4400022−2222−22040-400000000000000000022−2222−22000000000000000000000000000
χ5244-4-44400-4-4-44000−2222−2222040-4000000000000000000−2222−2222000000000000000000000000000
χ5344-4-44-4004-4-4400000000-4040000000000000000000000000−2i22i2−2i22i200000000000000000000
χ5444-4-44-4004-4-4400000000-40400000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5544-4-4-2400-422-200022−2222−220-20200000000000000023−230−22−220000000000000006−60000000000
χ5644-4-4-2400-422-200022−2222−220-202000000000000000−23230−22−22000000000000000−660000000000
χ5744-4-4-2400-422-2000−2222−22220-20200000000000000023−2302−22−2000000000000000−660000000000
χ5844-4-4-2400-422-2000−2222−22220-202000000000000000−232302−22−20000000000000006−60000000000
χ594-44-440000-44-40002i−2i−2i2i00004-400000000000000002i−2i−2i2i0002i−2i−2i2i00000000000000000000
χ604-44-440000-44-40002i−2i−2i2i0000-4400000000000000002i−2i−2i2i000−2i2i2i−2i00000000000000000000
χ614-44-440000-44-4000−2i2i2i−2i00004-40000000000000000−2i2i2i−2i000−2i2i2i−2i00000000000000000000
χ624-44-440000-44-4000−2i2i2i−2i0000-440000000000000000−2i2i2i−2i0002i−2i−2i2i00000000000000000000
χ634-4-4440-4404-4-4000000040-40004i−4i−4i4i0000000000000000000000000000000000000000000
χ644-4-4440-4404-4-4000000040-4000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-4-44-204-40-2224-40−2i2−2i22i22i220-2000000000000−2i22i2-22000i2i2−i2−i20000000000000i2−i2000000000000
χ664-4-44-204-40-2224-402i22i2−2i2−2i220-20000000000002i2−2i2-22000−i2−i2i2i20000000000000−i2i2000000000000
χ674-4-44-204-40-222-440−2i2−2i22i22i220-20000000000002i2−2i22-2000i2i2−i2−i20000000000000−i2i2000000000000
χ684-4-44-204-40-222-4402i22i2−2i2−2i220-2000000000000−2i22i22-2000−i2−i2i2i20000000000000i2−i2000000000000
χ6988-8-8-4-800844-40000000040-40000000000000000000000000000000000000000000000000
χ708-88-8-400004-440004i−4i−4i4i0000000000000000000000−2i2i2i−2i000000000000000000000000000
χ718-88-8-400004-44000−4i4i4i−4i00000000000000000000002i−2i−2i2i000000000000000000000000000
χ728-8-88-40-880-4440000000-40400000000000000000000000000000000000000000000000000

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