Finite Group Databasebeta

← Group #12430

Character table — Group #12430

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49
size1111222222222222222244444444444444444444444161616163232
order122244448888161616161616161622444888888161616161616161616161616888822
χ11111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1
χ6111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11
χ7111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111111111-1-1-11
χ8111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1111-1
χ922222222-2-2-2-20000000022222-2-2-2-2-2-2000000000000000000
χ1022222222-2-2-2-200000000-2-22-2-2-2-22222000000000000000000
χ1122222-2-2200002222−2−2−2−222-2-2-200000022−2−22222−2−2−2−2000000
χ1222222-2-2200002222−2−2−2−2-2-2-22200000022−2−2−2−2−2−22222000000
χ1322222-2-220000−2−2−2−2222222-2-2-2000000−2−222−2−2−2−22222000000
χ1422222-2-220000−2−2−2−22222-2-2-222000000−2−2222222−2−2−2−2000000
χ152222-222-222222222222200-200-2-20000-2-2-2-200000000000000
χ162222-222-22222-2-2-2-2-2-2-2-200-200-2-20000222200000000000000
χ172222-222-2-2-2-2-20000000000-20022000000002i2i−2i−2i2i2i−2i−2i000000
χ182222-222-2-2-2-2-20000000000-2002200000000−2i−2i2i2i−2i−2i2i2i000000
χ192222-2-2-2-200002222−2−2−2−200200002i2i−2i−2i−2−222i2i2−i2−i2−i2−i2i2i2000000
χ202222-2-2-2-200002222−2−2−2−20020000−2i−2i2i2i−2−222−i2−i2i2i2i2i2−i2−i2000000
χ212222-2-2-2-20000−2−2−2−2222200200002i2i−2i−2i22−2−2−i2−i2i2i2i2i2−i2−i2000000
χ222222-2-2-2-20000−2−2−2−222220020000−2i−2i2i2i22−2−2i2i2−i2−i2−i2−i2i2i2000000
χ2322-2-2200-22−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ50002i−2i2−2i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000
χ2422-2-2200-22−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000−2i2i2−2−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000
χ2522-2-2200-22−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ50002i−2i2−2i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000
χ2622-2-2200-22−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000−2i2i2−2−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000
χ2722-2-2200-2−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ70002i−2i−22−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000
χ2822-2-2200-2−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000−2i2i−22i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000
χ2922-2-2200-2−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ70002i−2i−22−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000
χ3022-2-2200-2−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000−2i2i−22i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000
χ3122-2-2-20022−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ52-2000−222−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5000000
χ3222-2-2-20022−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5-22000−22−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5000000
χ3322-2-2-20022−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ52-2000−222−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5000000
χ3422-2-2-20022−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5-22000−22−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5000000
χ3522-2-2-2002−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ72-20002−2−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7000000
χ3622-2-2-2002−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7-220002−22−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7000000
χ3722-2-2-2002−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ72-20002−2−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7000000
χ3822-2-2-2002−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7-220002−22−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7000000
χ392-2-220-220-2-2222-22-22-22-2000000000000000000000002−22−200
χ402-2-220-220-2-2222-22-22-22-200000000000000000000000−22−2200
χ412-2-220-220-2-222-22-22-22-22000000000000000000000002−2−2200
χ422-2-220-220-2-222-22-22-22-2200000000000000000000000−222−200
χ434-44-4000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000000
χ444-44-4000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000000
χ454-44-40000−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000
χ464-44-40000−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000
χ474-4-4404-40000022−2222−22−2222−222200000000000000000000000000000
χ484-4-4404-400000−2222−222222−2222−2200000000000000000000000000000
χ494-4-440-44044-4-40000000000000000000000000000000000000

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