Finite Group Databasebeta

← Group #490481

Character table — Group #490481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11222222222224444444444888888881616161632321122222222222444444444488888888161616163232
order12244888816161616448816161616161624881616161616161616222224488881616161644881616161616162488161616161616161622
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
χ5111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-1111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-1
χ6111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-11
χ7111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11
χ8111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-1
χ92222222-2-22222-2-2-2222-2-2-2-2000000000000002222222-2-22222-2-2-2222-2-2-2-200000000000000
χ102222222-2-2-2-2-2-2-2-2-22-2-22222000000000000002222222-2-2-2-2-2-2-2-2-22-2-2222200000000000000
χ1122222-2-2220000-2-22-200000022-2-2000000000022222-2-2220000-2-22-200000022-2-20000000000
χ1222222-2-2220000-2-22-2000000-2-222000000000022222-2-2220000-2-22-2000000-2-2220000000000
χ1322222-2-2-2-2000022-2-200000000002i2i−2i−2i00000022222-2-2-2-2000022-2-200000000002i2i−2i−2i000000
χ1422222-2-2-2-2000022-2-20000000000−2i−2i2i2i00000022222-2-2-2-2000022-2-20000000000−2i−2i2i2i000000
χ1522-22-2002222−2−200-202−222−2−22-2002−22−200000022-22-2002222−2−200-202−222−2−22-2002−22−2000000
χ1622-22-2002222−2−200-202−222−2−2-2200−22−2200000022-22-2002222−2−200-202−222−2−2-2200−22−22000000
χ1722-22-20022−2−22200-20−22−2−2222-200−22−2200000022-22-20022−2−22200-20−22−2−2222-200−22−22000000
χ1822-22-20022−2−22200-20−22−2−222-22002−22−200000022-22-20022−2−22200-20−22−2−222-22002−22−2000000
χ1922-22-200-2-222−2−200202−2−2−222002i−2ii2−i2−i2i200000022-22-200-2-222−2−200202−2−2−222002i−2ii2−i2−i2i2000000
χ2022-22-200-2-222−2−200202−2−2−22200−2i2i−i2i2i2−i200000022-22-200-2-222−2−200202−2−2−22200−2i2i−i2i2i2−i2000000
χ2122-22-200-2-2−2−2220020−2222−2−2002i−2i−i2i2i2−i200000022-22-200-2-2−2−2220020−2222−2−2002i−2i−i2i2i2−i2000000
χ2222-22-200-2-2−2−2220020−2222−2−200−2i2ii2−i2−i2i200000022-22-200-2-2−2−2220020−2222−2−200−2i2ii2−i2−i2i2000000
χ2322-2-2222002222000-2-2-20000000000002−22−20022-2-2222002222000-2-2-20000000000002−22−200
χ2422-2-2222002222000-2-2-2000000000000−22−220022-2-2222002222000-2-2-2000000000000−22−2200
χ2522-2-222200-2-2-2-2000-2220000000000002−2−220022-2-222200-2-2-2-2000-2220000000000002−2−2200
χ2622-2-222200-2-2-2-2000-222000000000000−222−20022-2-222200-2-2-2-2000-222000000000000−222−200
χ27444-4-400002222−22−220000−2222000000000000000000444-4-400002222−22−220000−2222000000000000000000
χ28444-4-40000−22−222222000022−22000000000000000000444-4-40000−22−222222000022−22000000000000000000
χ2944-4-44-4-400000000040000000000000000000044-4-44-4-4000000000400000000000000000000
χ304-400022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-20000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000004-400022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-20000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ314-400022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-20000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000004-400022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-20000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ324-400022−22−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000004-400022−22−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ334-400022−22−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000004-400022−22−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ344-4000−222222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000004-4000−222222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ354-4000−222222−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000004-4000−222222−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ364-4000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-20000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000004-4000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-20000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ374-4000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-20000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000004-4000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-20000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
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
χ42111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-11
χ43111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-11-1
χ44111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1111-1
χ45111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-11
χ462222222-2-22222-2-2-2222-2-2-2-200000000000000-2-2-2-2-2-2-222-2-2-2-2222-2-2-2222200000000000000
χ472222222-2-2-2-2-2-2-2-2-22-2-2222200000000000000-2-2-2-2-2-2-2222222222-222-2-2-2-200000000000000
χ4822222-2-2220000-2-22-200000022-2-20000000000-2-2-2-2-222-2-2000022-22000000-2-2220000000000
χ4922222-2-2220000-2-22-2000000-2-2220000000000-2-2-2-2-222-2-2000022-2200000022-2-20000000000
χ5022222-2-2-2-2000022-2-200000000002i2i−2i−2i000000-2-2-2-2-222220000-2-2220000000000−2i−2i2i2i000000
χ5122222-2-2-2-2000022-2-20000000000−2i−2i2i2i000000-2-2-2-2-222220000-2-22200000000002i2i−2i−2i000000
χ5222-22-2002222−2−200-202−222−2−22-2002−22−2000000-2-22-2200-2-2−2−2220020−22−2−222-2200−22−22000000
χ5322-22-2002222−2−200-202−222−2−2-2200−22−22000000-2-22-2200-2-2−2−2220020−22−2−2222-2002−22−2000000
χ5422-22-20022−2−22200-20−22−2−2222-200−22−22000000-2-22-2200-2-222−2−200202−222−2−2-22002−22−2000000
χ5522-22-20022−2−22200-20−22−2−222-22002−22−2000000-2-22-2200-2-222−2−200202−222−2−22-200−22−22000000
χ5622-22-200-2-222−2−200202−2−2−222002i−2ii2−i2−i2i2000000-2-22-220022−2−22200-20−2222−2−200−2i2i−i2i2i2−i2000000
χ5722-22-200-2-222−2−200202−2−2−22200−2i2i−i2i2i2−i2000000-2-22-220022−2−22200-20−2222−2−2002i−2ii2−i2−i2i2000000
χ5822-22-200-2-2−2−2220020−2222−2−2002i−2i−i2i2i2−i2000000-2-22-22002222−2−200-202−2−2−22200−2i2ii2−i2−i2i2000000
χ5922-22-200-2-2−2−2220020−2222−2−200−2i2ii2−i2−i2i2000000-2-22-22002222−2−200-202−2−2−222002i−2i−i2i2i2−i2000000
χ6022-2-2222002222000-2-2-20000000000002−22−200-2-222-2-2-200-2-2-2-2000222000000000000−22−2200
χ6122-2-2222002222000-2-2-2000000000000−22−2200-2-222-2-2-200-2-2-2-20002220000000000002−22−200
χ6222-2-222200-2-2-2-2000-2220000000000002−2−2200-2-222-2-2-20022220002-2-2000000000000−222−200
χ6322-2-222200-2-2-2-2000-222000000000000−222−200-2-222-2-2-20022220002-2-20000000000002−2−2200
χ64444-4-400002222−22−220000−2222000000000000000000-4-4-4440000−22−222222000022−22000000000000000000
χ65444-4-40000−22−222222000022−22000000000000000000-4-4-44400002222−22−220000−2222000000000000000000
χ6644-4-44-4-4000000000400000000000000000000-4-444-444000000000-400000000000000000000
χ674-400022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-20000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000-44000−2222−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ684-400022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-20000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000-44000−2222−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ694-400022−22−22222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000-44000−222222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-20000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ704-400022−22−2222−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000-44000−222222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-20000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ714-4000−222222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000-4400022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-20000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ724-4000−222222−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000-4400022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-20000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ734-4000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-20000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000-4400022−2222−22−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ744-4000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-20000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000-4400022−2222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000

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