Finite Group Databasebeta

← Group #100355

Character table — Group #100355

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888888888888888844
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
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111111-1-1-1-1-1-11-1-1-111-1-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111111-1-1-1-1-1-11-1-1-111-1-1-111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111111-1-1-1-1-1-11-1-1-111-1-1-111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111111-1-1-1-1-1-11-1-1-111-1-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111111-1-1-1-1-1-11-1-1-111-1-1-1-1-11-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111111-1-1-1-1-1-11-1-1-111-1-1-1-1-11-1-11111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111111-1-1-1-1-1-11-1-1-111-1-1-1-1-11-1-11111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111111-1-1-1-1-1-11-1-1-111-1-1-1-1-11-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ1722222222222222-2-2-222-22-2-2-2-2222-2-2-222-2-2000000000000000000000000000000
χ1822222222222222-2-2-222-22-2-2-2-22-2-2-222-2-222000000000000000000000000000000
χ1922222222222-2-2-22222-22-2-2-222-222-2-2-2-2-222000000000000000000000000000000
χ2022222222222-2-2-22222-22-2-2-222-2-2-2-22222-2-2000000000000000000000000000000
χ2122222222-2-2-2222222-222-222-2-2-200-20000002222-2-2-2-20000000000000000000000
χ2222222222-2-2-2222222-222-222-2-2-200-2000000-2-2-2-222220000000000000000000000
χ2322222222-2-2-2222-2-2-2-22-2-2-2-222-20020000000000000000000000000000002i−2i2i−2i00
χ2422222222-2-2-2222-2-2-2-22-2-2-2-222-2002000000000000000000000000000000−2i2i−2i2i00
χ2522222222-2-2-2-2-2-2222-2-222-2-2-2-220020000000000000000000000000000002-2-2200
χ2622222222-2-2-2-2-2-2222-2-222-2-2-2-22002000000000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2922-2-22-2-222-2-200022-220-20002-202-2000002-200000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i20000000000
χ3022-2-22-2-222-2-200022-220-20002-202-2000002-200000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i20000000000
χ3122-2-22-2-222-2-200022-220-20002-20-2200000-2200000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i20000000000
χ3222-2-22-2-222-2-200022-220-20002-20-2200000-2200000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i20000000000
χ3322-2-22-2-222-2-2000-2-22202000-2202-200000-220000000022−2−2−2−2222−2−220000000000
χ3422-2-22-2-222-2-2000-2-22202000-2202-200000-2200000000−2−22222−2−2−222−20000000000
χ3522-2-22-2-222-2-2000-2-22202000-220-22000002-20000000022−2−2−2−222−222−20000000000
χ3622-2-22-2-222-2-2000-2-22202000-220-22000002-200000000−2−22222−2−22−2−220000000000
χ372-2-2-2222-200022-22-2-20-2202-200000000000000002-22-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ382-2-2-2222-200022-22-2-20-2202-200000000000000002-22-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ392-2-2-2222-200022-22-2-20-2202-20000000000000000-22-22i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ402-2-2-2222-200022-22-2-20-2202-20000000000000000-22-22−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ412-2-2-2222-2000-2-22-22202-202-200000000000000002i−2i−2i2i2−22−2−22−220000−i2i2i2−i2000000
χ422-2-2-2222-2000-2-22-22202-202-200000000000000002i−2i−2i2i−22−222−22−20000i2−i2−i2i2000000
χ432-2-2-2222-2000-2-22-22202-202-20000000000000000−2i2i2i−2i2−22−2−22−220000i2−i2−i2i2000000
χ442-2-2-2222-2000-2-22-22202-202-20000000000000000−2i2i2i−2i−22−222−22−20000−i2i2i2−i2000000
χ45444-4-44-4-444-4000000-4000000000004-40000000000000000000000000000000000
χ46444-4-44-4-444-4000000-400000000000-440000000000000000000000000000000000
χ47444-4-44-4-4-4-44000000400000000000004i−4i00000000000000000000000000000000
χ48444-4-44-4-4-4-4400000040000000000000−4i4i00000000000000000000000000000000
χ4944-44-4-44-44-444-44000-4-40-400004000000000000000000000000000000000000000
χ5044-44-4-44-44-44-44-4000-44040000-4000000000000000000000000000000000000000
χ5144-44-4-44-4-44-44-440004-4040000-4000000000000000000000000000000000000000
χ5244-44-4-44-4-44-4-44-4000440-400004000000000000000000000000000000000000000
χ5344-4-44-4-44-44400044-4-40-4000-440000000000000000000000000000000000000000
χ5444-4-44-4-44-444000-4-44-4040004-40000000000000000000000000000000000000000
χ554-4444-4-4-40000004-4400-4000000000000000000000002-2-222-2-2200000000000000
χ564-4444-4-4-40000004-4400-400000000000000000000000-222-2-222-200000000000000
χ574-4444-4-4-4000000-44-4004000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ584-4444-4-4-4000000-44-400400000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ594-44-4-4-4440004-4-400004000000000000000022−2222−2200000000000000000000000000
χ604-44-4-4-4440004-4-4000040000000000000000−2222−222200000000000000000000000000
χ614-44-4-4-444000-4440000-400000000000000002i2−2i2−2i22i200000000000000000000000000
χ624-44-4-4-444000-4440000-40000000000000000−2i22i22i2−2i200000000000000000000000000
χ634-4-4-4444-400044-4-4440-4-40-44000000000000000000000000000000000000000000
χ644-4-4-4444-4000-4-444-4-40440-44000000000000000000000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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