Finite Group Databasebeta

← Group #122849

Character table — Group #122849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444888888888888888888888816161616323232323232
order122222448888444444444888888448888161616161616161616161616161616164444448888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1-1-111-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ6111111111111111-1-1-1-1-1-111-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ7111111111111111-1-1-1-1-1-111-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ8111111111111111-1-1-1-1-1-111-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ911111111-1-1-1-11-1-111-111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−ii−i
χ1011111111-1-1-1-11-1-111-111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-11−ii−ii
χ1111111111-1-1-1-11-1-111-111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii−ii
χ1211111111-1-1-1-11-1-111-111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-11i−ii−i
χ1311111111-1-1-1-11-1-1-1-11-1-11-1-11111-1111-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-11
χ1411111111-1-1-1-11-1-1-1-11-1-11-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-111-1
χ1511111111-1-1-1-11-1-1-1-11-1-11-1-11111-1111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-111-1
χ1611111111-1-1-1-11-1-1-1-11-1-11-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-11
χ172222222222222-2-222-222-2222222-2-2-2-2-2-200000000000000000000000000
χ182222222222222-2-2-2-22-2-2222-2-2-2-2-22-2-22200000000000000000000000000
χ1922222222-2-2-2-2222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000
χ2022222222-2-2-2-2222-2-2-2-2-2-2-2-222222-2-2-22200000000000000000000000000
χ21222222-2-20000-222222-2-22000000-2-2000022−2−222−2−222−2−222−2−20000000000
χ22222222-2-20000-222222-2-22000000-2-20000−2−222−2−222−2−222−2−2220000000000
χ23222222-2-20000-222-2-2-222-2000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000
χ24222222-2-20000-222-2-2-222-2000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000
χ25222222-2-20000-2-2-222-2-2-2-2000000220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ26222222-2-20000-2-2-222-2-2-2-2000000220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ27222222-2-20000-2-2-2-2-222220000002-2000022−2−2−2−222−2−22222−2−20000000000
χ28222222-2-20000-2-2-2-2-222220000002-20000−2−22222−2−222−2−2−2−2220000000000
χ292-22-22-20022−2−202-22-2200-22−222−2−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ302-22-22-20022−2−202-22-2200-22−222−2−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ312-22-22-20022−2−202-2-22-20022−2−2−222002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ322-22-22-20022−2−202-2-22-20022−2−2−222002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ332-22-22-20022−2−20-222-2-20022−222−2−200−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ342-22-22-20022−2−20-222-2-20022−222−2−200−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ352-22-22-20022−2−20-22-22200-22−2−2−22200−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ362-22-22-20022−2−20-22-22200-22−2−2−22200−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ372-22-22-200−2−22202-22-2200-2−22−2−22200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ382-22-22-200−2−22202-22-2200-2−22−2−22200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ392-22-22-200−2−22202-2-22-2002−2222−2−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ402-22-22-200−2−22202-2-22-2002−2222−2−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ412-22-22-200−2−2220-222-2-2002−22−2−222002−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ422-22-22-200−2−2220-222-2-2002−22−2−222002−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ432-22-22-200−2−2220-22-22200-2−2222−2−2002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ442-22-22-200−2−2220-22-22200-2−2222−2−2002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ454444-4-4444444-400000000-4-4000000000000000000000000000000000000
χ464444-4-444-4-4-4-4-40000000044000000000000000000000000000000000000
χ474444-4-4-4-40000400000000004i−4i4i−4i00000000000000000000000000000000
χ484444-4-4-4-4000040000000000−4i4i−4i4i00000000000000000000000000000000
χ4944-4-4004-44-44-400000000000000000000000000000000000002-22-2000000
χ5044-4-4004-44-44-40000000000000000000000000000000000000-22-22000000
χ5144-4-4004-4-44-4400000000000000000000000000000000000002-2-22000000
χ5244-4-4004-4-44-440000000000000000000000000000000000000-222-2000000
χ534-44-4-44002222−22−220000004i−4i0−22222i2−2i2−2i22i200000000000000000000000000000000
χ544-44-4-44002222−22−22000000−4i4i0−2222−2i22i22i2−2i200000000000000000000000000000000
χ554-44-4-4400−22−2222220000004i−4i022−22−2i22i22i2−2i200000000000000000000000000000000
χ564-44-4-4400−22−222222000000−4i4i022−222i2−2i2−2i22i200000000000000000000000000000000
χ5788-8-800-88000000000000000000000000000000000000000000000000000
χ588-8-88000042−42−424200000000000000000000000000000000000000000000000
χ598-8-880000−424242−4200000000000000000000000000000000000000000000000

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