Finite Group Databasebeta

← Group #10772495

Character table — Group #10772495

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222444444444446666668888888888888888121212121212121616161616161616161624242424242424324848
order122234444666444888812121212224444444448812121212122424242444488882812121212242424242444488648
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11-1-1-111-1-111111111111111-1-1-11-1-111-1-1-1-1-1-1111-1-1-1
χ311111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11-1-1
χ411111111111111111111111-1-1-1-1-1-1-11-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-111
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
χ6111111111111111-1-1-1-11111111111-11-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111-11-1-1-1-111-1-1-1-11-1-1111
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
χ8111111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111-11-1-1-1-1111111-1111-1-1
χ9111111111111-1-11111111111111111-1-1-11-1-111-1-1111111-1-11111-111-1-1-1-1-1111-1-11-1-1-1-1-11
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
χ11111111111111-1-1111111111-1-1-1-1-1-11-1-1-11-1-111-1-111111-111-1-1-1-1-111-1-1-1-1-111-111-1111-11-1
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
χ13111111111111-1-11-1-1-1-111111111111-1-1-111111-1-11-1-1-1-11-1-1-1-1-1-11-11-1-1-111-1-11-1-11-11111-1
χ14111111111111-1-11-1-1-1-11111111111-1-111-111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-11-1-1111111-111-1-111-1-11
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-11-1-1-111111-1-11-1-1-1-1-11111111-11-1-1-111-1-1-111-11-1-11-11
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11-1-1-1-1-1111111-11-1-11111111-1-111-1-1-11-1
χ17222222-2-2222200-200002-22-22222-2-22000-2002200-20000-200000000-20000000-2002000000
χ18222222-2-2222200-200002-22-22222-2-2-2000200-2-200-20000-20000000020000000200-2000000
χ19222222-2-2222200-200002-22-2-2-2-2-2222000-2002200-20000200000000-20000000200-2000000
χ20222222-2-2222200-200002-22-2-2-2-2-222-2000200-2-200-2000020000000020000000-2002000000
χ2122222-222-222222-20000-22-2222-2-2-2-20-2000000022-200002-2-20000000-20000000000200000
χ2222222-222-222222-20000-22-22-2-222220-2000000022-20000-2220000000-20000000000-200000
χ2322222-222-2222-2-2-20000-22-2222-2-2-2-2020000000-2-2-20000222000000020000000000-200000
χ2422222-222-2222-2-2-20000-22-22-2-22222020000000-2-2-20000-2-2-2000000020000000000200000
χ2522222-2-2-2-22220020000-2-2-2-222-2-222002-2000000020000-200000000002-2000002-20000000
χ2622222-2-2-2-22220020000-2-2-2-222-2-22200-22000000020000-20000000000-2200000-220000000
χ2722222-2-2-2-22220020000-2-2-2-2-2-222-2-2002-2000000020000200000000002-200000-220000000
χ2822222-2-2-2-22220020000-2-2-2-2-2-222-2-200-2200000002000020000000000-22000002-20000000
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
χ302222-12222-1-1-12222222-1-1-1-1000000-22-2-2-22211-1-1-1-1-1-1-10000000-2-21-111-1-1110000000100
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
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1000000-22-2-2-2-2-211-1-1-111110000000221-11111-1-10000000-100
χ332222-12222-1-1-1-2-222222-1-1-1-10000002-2-2-22-2-2-1-111-1-1-1-1-10000000-22-111111-1-10000000100
χ342222-12222-1-1-1-2-222222-1-1-1-1000000-2-222-2-2-21111-1-1-1-1-100000002-211-1-111110000000-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-10000002-2-2-2222-1-111-1111100000002-2-1111-1-1110000000-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1000000-2-222-2221111-111110000000-2211-1-1-1-1-1-10000000100
χ372-22-220-220-2-222i−2i022−2−2020-2002i−2i2i−2i00000−i2i2002i−2i022−2−202-2−i2−i2i2i2000000−i2i200000002−2000
χ382-22-220-220-2-222i−2i022−2−2020-200−2i2i−2i2i00000−i2i2002i−2i022−2−20-22i2i2−i2−i2000000−i2i20000000−22000
χ392-22-220-220-2-222i−2i0−2−222020-2002i−2i2i−2i00000i2−i2002i−2i0−2−22202-2i2i2−i2−i2000000i2−i20000000−22000
χ402-22-220-220-2-222i−2i0−2−222020-200−2i2i−2i2i00000i2−i2002i−2i0−2−2220-22−i2−i2i2i2000000i2−i200000002−2000
χ412-22-220-220-2-22−2i2i022−2−2020-2002i−2i2i−2i00000i2−i200−2i2i022−2−20-22−i2−i2i2i2000000i2−i20000000−22000
χ422-22-220-220-2-22−2i2i022−2−2020-200−2i2i−2i2i00000i2−i200−2i2i022−2−202-2i2i2−i2−i2000000i2−i200000002−2000
χ432-22-220-220-2-22−2i2i0−2−222020-2002i−2i2i−2i00000−i2i200−2i2i0−2−2220-22i2i2−i2−i2000000−i2i200000002−2000
χ442-22-220-220-2-22−2i2i0−2−222020-200−2i2i−2i2i00000−i2i200−2i2i0−2−22202-2−i2−i2i2i2000000−i2i20000000−22000
χ454444-24-4-44-2-2-200-40000-22-220000004000-400-2-20020000000000000200000000000000000
χ464444-24-4-44-2-2-200-40000-22-22000000-4000400220020000000000000-200000000000000000
χ474444-2-444-4-2-2-244-400002-22-20000000-40000000-2-220000000000000020000000000000000
χ484444-2-444-4-2-2-2-4-4-400002-22-200000004000000022200000000000000-20000000000000000
χ494444-2-4-4-4-4-2-2-200400002222000000004-40000000-2000000000000000-2200000000000000
χ504444-2-4-4-4-4-2-2-20040000222200000000-440000000-20000000000000002-200000000000000
χ5144-4-44400-44-4-4000000040-40000000000000000000000000022−2222−2200000000000000000000
χ5244-4-44400-44-4-4000000040-400000000000000000000000000−2222−222200000000000000000000
χ5344-4-44-40044-4-4000−2i22i2−2i22i2-4040000000000000000000−2i22i2−2i22i2000000000000000000000000000
χ5444-4-44-40044-4-40002i2−2i22i2−2i2-40400000000000000000002i2−2i22i2−2i2000000000000000000000000000
χ5544-4-4-2-4004-222000−2i22i2−2i22i220-200000000000000−2i32i3000i2−i2i2−i20000000000000006−60000000000
χ5644-4-4-2-4004-222000−2i22i2−2i22i220-2000000000000002i3−2i3000i2−i2i2−i2000000000000000−660000000000
χ5744-4-4-2-4004-2220002i2−2i22i2−2i220-200000000000000−2i32i3000−i2i2−i2i2000000000000000−660000000000
χ5844-4-4-2-4004-2220002i2−2i22i2−2i220-2000000000000002i3−2i3000−i2i2−i2i20000000000000006−60000000000
χ594-44-4404-40-4-4400000000-404004i−4i−4i4i0000000000000000000000000000000000000000000
χ604-44-4404-40-4-4400000000-40400−4i4i4i−4i0000000000000000000000000000000000000000000
χ614-44-4-20-44022-24i−4i02222−22−220-20200000000000−2i22i200−2i2i0−2−2220000000000000i2−i2000000000000
χ624-44-4-20-44022-24i−4i0−22−2222220-202000000000002i2−2i200−2i2i022−2−20000000000000−i2i2000000000000
χ634-44-4-20-44022-2−4i4i02222−22−220-202000000000002i2−2i2002i−2i0−2−2220000000000000−i2i2000000000000
χ644-44-4-20-44022-2−4i4i0−22−2222220-20200000000000−2i22i2002i−2i022−2−20000000000000i2−i2000000000000
χ654-4-4440000-44-40002i−2i−2i2i00004-400000000000000002i−2i−2i2i0002i−2i−2i2i00000000000000000000
χ664-4-4440000-44-40002i−2i−2i2i0000-4400000000000000002i−2i−2i2i000−2i2i2i−2i00000000000000000000
χ674-4-4440000-44-4000−2i2i2i−2i00004-40000000000000000−2i2i2i−2i000−2i2i2i−2i00000000000000000000
χ684-4-4440000-44-4000−2i2i2i−2i0000-440000000000000000−2i2i2i−2i0002i−2i−2i2i00000000000000000000
χ6988-8-8-4800-8-4440000000-40400000000000000000000000000000000000000000000000000
χ708-88-8-408-8044-40000000040-40000000000000000000000000000000000000000000000000
χ718-8-88-400004-440004i−4i−4i4i0000000000000000000000−2i2i2i−2i000000000000000000000000000
χ728-8-88-400004-44000−4i4i4i−4i00000000000000000000002i−2i−2i2i000000000000000000000000000

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