Finite Group Databasebeta

← Group #490609

Character table — Group #490609

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244444444444888888881616161632321111222222224444444444488888888161616163232
order12224444888848816161616161616164488161616168888442222444488884881616161616161616448816161616888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111111111111111111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1
χ6111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1
χ922222222-2-2-2-22-2-20000000022-2-2000000000022222222-2-2-2-22-2-20000000022-2-20000000000
χ1022222222-2-2-2-22-2-200000000-2-222000000000022222222-2-2-2-22-2-200000000-2-2220000000000
χ1122222-2-220000-20022−2−222−2−22-20022−2−200000022222-2-220000-20022−2−222−2−22-20022−2−2000000
χ1222222-2-220000-20022−2−222−2−2-2200−2−22200000022222-2-220000-20022−2−222−2−2-2200−2−222000000
χ1322222-2-220000-200−2−222−2−2222-200−2−22200000022222-2-220000-200−2−222−2−2222-200−2−222000000
χ1422222-2-220000-200−2−222−2−222-220022−2−200000022222-2-220000-200−2−222−2−222-220022−2−2000000
χ152222-222-22222-2-2-22222-2-2-2-2000000000000002222-222-22222-2-2-22222-2-2-2-200000000000000
χ162222-222-22222-2-2-2-2-2-2-22222000000000000002222-222-22222-2-2-2-2-2-2-2222200000000000000
χ172222-222-2-2-2-2-2-2220000000000002i−2i2i−2i0000002222-222-2-2-2-2-2-2220000000000002i−2i2i−2i000000
χ182222-222-2-2-2-2-2-222000000000000−2i2i−2i2i0000002222-222-2-2-2-2-2-222000000000000−2i2i−2i2i000000
χ192222-2-2-2-2000020022−2−2−2−222002i−2ii2−i2−i2i20000002222-2-2-2-2000020022−2−2−2−222002i−2ii2−i2−i2i2000000
χ202222-2-2-2-2000020022−2−2−2−22200−2i2i−i2i2i2−i20000002222-2-2-2-2000020022−2−2−2−22200−2i2i−i2i2i2−i2000000
χ212222-2-2-2-20000200−2−22222−2−2002i−2i−i2i2i2−i20000002222-2-2-2-20000200−2−22222−2−2002i−2i−i2i2i2−i2000000
χ222222-2-2-2-20000200−2−22222−2−200−2i2ii2−i2−i2i20000002222-2-2-2-20000200−2−22222−2−200−2i2ii2−i2−i2i2000000
χ2322-2-202-2022-2-20002-22-20000000000002−22−20022-2-202-2022-2-20002-22-20000000000002−22−200
χ2422-2-202-2022-2-20002-22-2000000000000−22−220022-2-202-2022-2-20002-22-2000000000000−22−2200
χ2522-2-202-2022-2-2000-22-220000000000002−2−220022-2-202-2022-2-2000-22-220000000000002−2−2200
χ2622-2-202-2022-2-2000-22-22000000000000−222−20022-2-202-2022-2-2000-22-22000000000000−222−200
χ2744-4-404-40-4-444000000000000000000000000044-4-404-40-4-4440000000000000000000000000
χ2844-4-40-440000000022−22−222200000000000000000044-4-40-440000000022−22−2222000000000000000000
χ2944-4-40-4400000000−222222−2200000000000000000044-4-40-4400000000−222222−22000000000000000000
χ304-44-4000022−2222−2200000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000004-44-4000022−2222−2200000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000
χ314-44-4000022−2222−220000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000004-44-4000022−2222−220000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000
χ324-44-40000−2222−222200000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000004-44-40000−2222−222200000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000
χ334-44-40000−2222−22220000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000004-44-40000−2222−22220000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000
χ344-4-44400-422−22−2222022−2200000000000000000000004-4-44400-422−22−2222022−220000000000000000000000
χ354-4-44400-4−222222−220−222200000000000000000000004-4-44400-4−222222−220−22220000000000000000000000
χ364-4-44-400422−22−22220−222200000000000000000000004-4-44-400422−22−22220−22220000000000000000000000
χ374-4-44-4004−222222−22022−2200000000000000000000004-4-44-4004−222222−22022−220000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ391111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ4011111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ42111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-11
χ43111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1
χ44111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111-1
χ45111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-11
χ4622222222-2-2-2-22-2-20000000022-2-20000000000-2-2-2-2-2-2-2-22222-22200000000-2-2220000000000
χ4722222222-2-2-2-22-2-200000000-2-2220000000000-2-2-2-2-2-2-2-22222-2220000000022-2-20000000000
χ4822222-2-220000-20022−2−222−2−22-20022−2−2000000-2-2-2-2-222-20000200−2−222−2−222-2200−2−222000000
χ4922222-2-220000-20022−2−222−2−2-2200−2−222000000-2-2-2-2-222-20000200−2−222−2−2222-20022−2−2000000
χ5022222-2-220000-200−2−222−2−2222-200−2−222000000-2-2-2-2-222-2000020022−2−222−2−2-220022−2−2000000
χ5122222-2-220000-200−2−222−2−222-220022−2−2000000-2-2-2-2-222-2000020022−2−222−2−22-200−2−222000000
χ522222-222-22222-2-2-22222-2-2-2-200000000000000-2-2-2-22-2-22-2-2-2-2222-2-2-2-2222200000000000000
χ532222-222-22222-2-2-2-2-2-2-2222200000000000000-2-2-2-22-2-22-2-2-2-22222222-2-2-2-200000000000000
χ542222-222-2-2-2-2-2-2220000000000002i−2i2i−2i000000-2-2-2-22-2-2222222-2-2000000000000−2i2i−2i2i000000
χ552222-222-2-2-2-2-2-222000000000000−2i2i−2i2i000000-2-2-2-22-2-2222222-2-20000000000002i−2i2i−2i000000
χ562222-2-2-2-2000020022−2−2−2−222002i−2ii2−i2−i2i2000000-2-2-2-222220000-200−2−22222−2−200−2i2i−i2i2i2−i2000000
χ572222-2-2-2-2000020022−2−2−2−22200−2i2i−i2i2i2−i2000000-2-2-2-222220000-200−2−22222−2−2002i−2ii2−i2−i2i2000000
χ582222-2-2-2-20000200−2−22222−2−2002i−2i−i2i2i2−i2000000-2-2-2-222220000-20022−2−2−2−22200−2i2ii2−i2−i2i2000000
χ592222-2-2-2-20000200−2−22222−2−200−2i2ii2−i2−i2i2000000-2-2-2-222220000-20022−2−2−2−222002i−2i−i2i2i2−i2000000
χ6022-2-202-2022-2-20002-22-20000000000002−22−200-2-2220-220-2-222000-22-22000000000000−22−2200
χ6122-2-202-2022-2-20002-22-2000000000000−22−2200-2-2220-220-2-222000-22-220000000000002−22−200
χ6222-2-202-2022-2-2000-22-220000000000002−2−2200-2-2220-220-2-2220002-22-2000000000000−222−200
χ6322-2-202-2022-2-2000-22-22000000000000−222−200-2-2220-220-2-2220002-22-20000000000002−2−2200
χ6444-4-404-40-4-4440000000000000000000000000-4-4440-44044-4-40000000000000000000000000
χ6544-4-40-440000000022−22−2222000000000000000000-4-44404-400000000−222222−22000000000000000000
χ6644-4-40-4400000000−222222−22000000000000000000-4-44404-40000000022−22−2222000000000000000000
χ674-44-4000022−2222−2200000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000-44-440000−2222−22220000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000
χ684-44-4000022−2222−220000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000-44-440000−2222−222200000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000
χ694-44-40000−2222−222200000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000-44-44000022−2222−220000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000
χ704-44-40000−2222−22220000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000-44-44000022−2222−2200000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000
χ714-4-44400-422−22−2222022−220000000000000000000000-444-4-4004−222222−220−22220000000000000000000000
χ724-4-44400-4−222222−220−22220000000000000000000000-444-4-400422−22−2222022−220000000000000000000000
χ734-4-44-400422−22−22220−22220000000000000000000000-444-4400-4−222222−22022−220000000000000000000000
χ744-4-44-4004−222222−22022−220000000000000000000000-444-4400-422−22−22220−22220000000000000000000000

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