Finite Group Databasebeta

← Group #152166

Character table — Group #152166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order124422244488882244881616161616161616881616161632323232323232323232323232323232222244448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ711111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ811111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ911-1-11-1-111-1-1-1111-11-11-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−i
χ1011-1-11-1-111-1-1-1111-11-11-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii
χ1111-1-11-1-111-1-1-1111-11-11-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii
χ1211-1-11-1-111-1-1-1111-11-11-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−i
χ1311-1-11-1-111-1-1-111-11-111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11i−i−ii
χ1411-1-11-1-111-1-1-111-11-111-11111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−iii−i
χ1511-1-11-1-111-1-1-111-11-111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−iii−i
χ1611-1-11-1-111-1-1-111-11-111-11111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−i−ii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ192222222222-2-2-2-22222-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-22222-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ2322222-2-2-2-2200002-2-220022−2−222−2−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ2422222-2-2-2-2200002-2-220022−2−222−2−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ2522222-2-2-2-2200002-2-2200−2−222−2−22200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ2622222-2-2-2-2200002-2-2200−2−222−2−22200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ2722222-2-2-2-220000-222-20022−2−222−2−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ2822222-2-2-2-220000-222-20022−2−222−2−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ2922222-2-2-2-220000-222-200−2−222−2−222002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3022222-2-2-2-220000-222-200−2−222−2−222002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ312222-22-2-22-222220000-2-22-22-22-22-200000000000000000000002-200-22000000
χ322222-22-2-22-222220000-2-22-22-22-22-20000000000000000000000-22002-2000000
χ332222-22-2-22-222220000-2-2-22-22-22-220000000000000000000000002-200-220000
χ342222-22-2-22-222220000-2-2-22-22-22-22000000000000000000000000-22002-20000
χ3522-2-2222-2-2-2000022-2-20022−2−2−2−222002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3622-2-2222-2-2-2000022-2-20022−2−2−2−222002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3722-2-2222-2-2-2000022-2-200−2−22222−2−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3822-2-2222-2-2-2000022-2-200−2−22222−2−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3922-2-2222-2-2-20000-2-2220022−2−2−2−22200−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ4022-2-2222-2-2-20000-2-2220022−2−2−2−22200−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4122-2-2222-2-2-20000-2-22200−2−22222−2−2002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4222-2-2222-2-2-20000-2-22200−2−22222−2−2002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4322-2-22-2-222-222-2-22-22-2-2200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ4422-2-22-2-222-222-2-22-22-2-2200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ4522-2-22-2-222-222-2-2-22-22-22000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ4622-2-22-2-222-222-2-2-22-22-22000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ4722-2-22-2-222-2-2-2222-22-22-2-2-2-2-222222-2-2-2220000000000000000000000000000
χ4822-2-22-2-222-2-2-222-22-222-2-2-2-2-22222-2222-2-20000000000000000000000000000
χ4922-2-2-2-22-222-2-2220000-222-22-2-22-2200000000000000000000002200-2-2000000
χ5022-2-2-2-22-222-2-2220000-222-22-2-22-220000000000000000000000-2-20022000000
χ5122-2-2-2-22-222-2-2220000-22-22-222-22-20000000000000000000000002200-2-20000
χ5222-2-2-2-22-222-2-2220000-22-22-222-22-2000000000000000000000000-2-200220000
χ534444-44-4-44-4-4-4-4-4000044000000000000000000000000000000000000000000
χ544444-4-444-4-4000000000022−22−222222−22−22220000000000000000000000000000000000
χ554444-4-444-4-40000000000−222222−22−222222−220000000000000000000000000000000000
χ5644-4-4-44-44-44000000000022−22−2222−222222−220000000000000000000000000000000000
χ5744-4-4-44-44-440000000000−222222−2222−22−22220000000000000000000000000000000000
χ5844-4-4-4-44-44444-4-400004-4000000000000000000000000000000000000000000
χ598-88i−8i0000004i2−4i242−42000000000000000000000000000000000000000000000000
χ608-88i−8i000000−4i24i2−4242000000000000000000000000000000000000000000000000
χ618-8−8i8i0000004i2−4i2−4242000000000000000000000000000000000000000000000000
χ628-8−8i8i000000−4i24i242−42000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.