Finite Group Databasebeta

← Group #100361

Character table — Group #100361

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-1-1111-1-11-111-1-1-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111-1-1-1-1-1111-1-11-111-1-1-1-111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111-1-1-1-1-1111-1-11-111-1-1-1-111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111-1-1-1-1-1111-1-11-111-1-1-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111-1-1-1-1-1111-1-11-111-1-1-1-11-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111-1-1-1-1-1111-1-11-111-1-1-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111-1-1-1-1-1111-1-11-111-1-1-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111-1-1-1-1-1111-1-11-111-1-1-1-11-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ172222222222222-2-2-222-2222-2-2-2-2-2000000002222-2-2-2-20000000000000000000000
χ182222222222222-2-2-222-2222-2-2-2-2-200000000-2-2-2-222220000000000000000000000
χ1922222222222-2-2222-222-2-2-22-2-22-222-2-222-2-2000000000000000000000000000000
χ2022222222222-2-2222-222-2-2-22-2-22-2-2-222-2-222000000000000000000000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-2-222-22000000000000000000000000000000002i−2i2i−2i00
χ2222222222222-2-2-2-2-2-22-2-2-2-2-222-2200000000000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2222222-222-2-2-222-2-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2222222-222-2-2-222-2-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-222-2-2-22-2-22-2-22-2-222000000000000000000000000000000002-2-2200
χ2622222222-2-2-222-2-2-22-2-22-2-22-2-22200000000000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ292222-2-2-2-222-22-20002-20-22-200000000000002-22-2000022−2−222−2−200002−22−2000000
χ302222-2-2-2-222-22-20002-20-22-200000000000002-22-20000−2−222−2−2220000−22−22000000
χ312222-2-2-2-222-22-20002-20-22-20000000000000-22-22000022−2−222−2−20000−22−22000000
χ322222-2-2-2-222-22-20002-20-22-20000000000000-22-220000−2−222−2−22200002−22−2000000
χ332222-2-2-2-2-2-22-22000-22022-200000000000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i200002−2−22000000
χ342222-2-2-2-2-2-22-22000-22022-200000000000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000−222−2000000
χ352222-2-2-2-2-2-22-22000-22022-20000000000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000−222−2000000
χ362222-2-2-2-2-2-22-22000-22022-20000000000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i200002−2−22000000
χ3722-2-22-2-22000222-2-2-202-20002-2002-200002-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ3822-2-22-2-22000222-2-2-202-20002-2002-200002-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ3922-2-22-2-22000222-2-2-202-20002-200-220000-2200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ4022-2-22-2-22000222-2-2-202-20002-200-220000-2200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4122-2-22-2-22000-2-22-2-22022000-22002-20000-22000000002−22−2−22−222−2−220000000000
χ4222-2-22-2-22000-2-22-2-22022000-22002-20000-2200000000−22−222−22−2−222−20000000000
χ4322-2-22-2-22000-2-22-2-22022000-2200-2200002-2000000002−22−2−22−22−222−20000000000
χ4422-2-22-2-22000-2-22-2-22022000-2200-2200002-200000000−22−222−22−22−2−220000000000
χ454444-4-4-4-444-4-44000-4-404-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-4000440-4-440000000000000000000000000000000000000000000
χ4744-4-44-4-4400044-444-40-4-4000-440000000000000000000000000000000000000000
χ4844-4-44-4-44000-4-4-44440-440004-40000000000000000000000000000000000000000
χ4944-4-4-444-40004-4000-4004000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5044-4-4-444-40004-4000-400400000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5144-4-4-444-4000-44000400-4000000000000000000000002-2-22-222-200000000000000
χ5244-4-4-444-4000-44000400-400000000000000000000000-222-22-2-2200000000000000
χ534-44-444-4-44-44000000-400000000000000000000022−2222−220000000000000000000000
χ544-44-444-4-44-44000000-4000000000000000000000−2222−22220000000000000000000000
χ554-44-444-4-4-44-400000040000000000000000000002i2−2i2−2i22i20000000000000000000000
χ564-44-444-4-4-44-40000004000000000000000000000−2i22i22i2−2i20000000000000000000000
χ574-44-4-4-4444-4-40044-404-4000-4004000000000000000000000000000000000000000
χ584-44-4-4-4444-4-400-4-44044000400-4000000000000000000000000000000000000000
χ594-44-4-4-444-4440044-40-4-4000400-4000000000000000000000000000000000000000
χ604-44-4-4-444-44400-4-440-44000-4004000000000000000000000000000000000000000
χ614-4-44-44-44000004-4400-400000000004i−4i0000000000000000000000000000000000
χ624-4-44-44-44000004-4400-40000000000−4i4i0000000000000000000000000000000000
χ634-4-44-44-4400000-44-40040000000000004-400000000000000000000000000000000
χ644-4-44-44-4400000-44-4004000000000000-4400000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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