Finite Group Databasebeta

← Group #100331

Character table — Group #100331

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
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111111-1-1-1-1-1-11-1-1-1-1-111-11111-1-1-1-11ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111111-1-1-1-1-1-11-1-1-1-1-111-11111-1-1-1-11ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111111-1-1-1-1-1-11-1-1-1-1-111-11111-1-1-1-11−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111111-1-1-1-1-1-11-1-1-1-1-111-11111-1-1-1-11−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-111111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-111111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-111111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-111111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ1722222222222222-2-2-222-22-2-2-2-2222-2-222-2-2-2000000000000000000000000000000
χ1822222222222222-2-2-222-22-2-2-2-22-2-222-2-222-2000000000000000000000000000000
χ1922222222222-2-2-22222-22-222-2-2-222-2-2-2-222-2000000000000000000000000000000
χ2022222222222-2-2-22222-22-222-2-2-2-2-22222-2-2-2000000000000000000000000000000
χ2122222222-2-2-2222222-222-2-2-222-200000000-22222-2-2-2-20000000000000000000000
χ2222222222-2-2-2222222-222-2-2-222-200000000-2-2-2-2-222220000000000000000000000
χ2322222222-2-2-2222-2-2-2-22-2-222-2-2-20000000020000000000000000000000002i−2i2i−2i00
χ2422222222-2-2-2222-2-2-2-22-2-222-2-2-2000000002000000000000000000000000−2i2i−2i2i00
χ2522222222-2-2-2-2-2-2222-2-222-2-2-2-220000000020000000000000000000000002-2-2200
χ2622222222-2-2-2-2-2-2222-2-222-2-2-2-22000000002000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-22i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ29222-22-2-2-222-200022-2-20-202-20002-200002-200000000022−2−222−2−22−22−20000000000
χ30222-22-2-2-222-200022-2-20-202-20002-200002-2000000000−2−222−2−222−22−220000000000
χ31222-22-2-2-222-200022-2-20-202-2000-220000-2200000000022−2−222−2−2−22−220000000000
χ32222-22-2-2-222-200022-2-20-202-2000-220000-22000000000−2−222−2−2222−22−20000000000
χ33222-22-2-2-222-2000-2-22-2020-220002-20000-22000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i20000000000
χ34222-22-2-2-222-2000-2-22-2020-220002-20000-22000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i20000000000
χ35222-22-2-2-222-2000-2-22-2020-22000-2200002-2000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i20000000000
χ36222-22-2-2-222-2000-2-22-2020-22000-2200002-2000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i20000000000
χ372-2-2-2222-200022-22-2-20-220002-2000000000000002-22-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ382-2-2-2222-200022-22-2-20-220002-2000000000000002-22-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ392-2-2-2222-200022-22-2-20-220002-200000000000000-22-22i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ402-2-2-2222-200022-22-2-20-220002-200000000000000-22-22−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ412-2-2-2222-2000-2-22-22202-20002-2000000000000002i−2i−2i2i2−22−2−22−220000−i2i2i2−i2000000
χ422-2-2-2222-2000-2-22-22202-20002-2000000000000002i−2i−2i2i−22−222−22−20000i2−i2−i2i2000000
χ432-2-2-2222-2000-2-22-22202-20002-200000000000000−2i2i2i−2i2−22−2−22−220000i2−i2−i2i2000000
χ442-2-2-2222-2000-2-22-22202-20002-200000000000000−2i2i2i−2i−22−222−22−20000−i2i2i2−i2000000
χ45444-44-4-4-4-4-4400044-440-40-44000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44000-4-4440404-4000000000000000000000000000000000000000000
χ4744-44-44-4-44-444-44000-4-40-400004000000000000000000000000000000000000000
χ4844-44-44-4-44-44-44-4000-44040000-4000000000000000000000000000000000000000
χ4944-44-44-4-4-44-44-440004-4040000-4000000000000000000000000000000000000000
χ5044-44-44-4-4-44-4-44-4000440-400004000000000000000000000000000000000000000
χ5144-4-4-4-4444-4-4000000400000000004-400000000000000000000000000000000000
χ5244-4-4-4-4444-4-400000040000000000-4400000000000000000000000000000000000
χ5344-4-4-4-444-444000000-40000000000004i−4i000000000000000000000000000000000
χ5444-4-4-4-444-444000000-4000000000000−4i4i000000000000000000000000000000000
χ554-44-4-44-440004-4-400004000000000000000022−2222−2200000000000000000000000000
χ564-44-4-44-440004-4-4000040000000000000000−2222−222200000000000000000000000000
χ574-44-4-44-44000-4440000-400000000000000002i2−2i2−2i22i200000000000000000000000000
χ584-44-4-44-44000-4440000-40000000000000000−2i22i22i2−2i200000000000000000000000000
χ594-4-444-4-440000004-4400-4000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ604-4-444-4-440000004-4400-400000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ614-4-444-4-44000000-44-4004000000000000000000000002-2-22-222-200000000000000
χ624-4-444-4-44000000-44-400400000000000000000000000-222-22-2-2200000000000000
χ634-4-4-4444-400044-4-4440-4-4000-440000000000000000000000000000000000000000
χ644-4-4-4444-4000-4-444-4-4044000-440000000000000000000000000000000000000000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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