Finite Group Databasebeta

← Group #490713

Character table — Group #490713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222244444444444888888881616161632321111222222224444444444488888888161616163232
order122244448888488888888881616161616161616248824222244448888488888888881616161616161616248824
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
χ922222222-2-2-2-22-2-22222-2-2-2-20000000000000022222222-2-2-2-22-2-22222-2-2-2-200000000000000
χ1022222222-2-2-2-22-2-2-2-2-2-222220000000000000022222222-2-2-2-22-2-2-2-2-2-2222200000000000000
χ1122222-2-220000-20022-2-2000022−2−222−2−200000022222-2-220000-20022-2-2000022−2−222−2−2000000
χ1222222-2-220000-20022-2-20000−2−222−2−22200000022222-2-220000-20022-2-20000−2−222−2−222000000
χ1322222-2-220000-200-2-222000022−2−2−2−22200000022222-2-220000-200-2-222000022−2−2−2−222000000
χ1422222-2-220000-200-2-2220000−2−22222−2−200000022222-2-220000-200-2-2220000−2−22222−2−2000000
χ152222-222-22222-2-2-200000000000000002-200002222-222-22222-2-2-200000000000000002-20000
χ162222-222-22222-2-2-20000000000000000-2200002222-222-22222-2-2-20000000000000000-220000
χ172222-222-2-2-2-2-2-2220000000000000000002i−2i002222-222-2-2-2-2-2-2220000000000000000002i−2i00
χ182222-222-2-2-2-2-2-222000000000000000000−2i2i002222-222-2-2-2-2-2-222000000000000000000−2i2i00
χ192-22-2200-222−2−202−2002i−2ii2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000002-22-2200-222−2−202−2002i−2ii2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ202-22-2200-222−2−202−2002i−2ii2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000002-22-2200-222−2−202−2002i−2ii2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ212-22-2200-222−2−202−200−2i2i−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000002-22-2200-222−2−202−200−2i2i−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ222-22-2200-222−2−202−200−2i2i−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000002-22-2200-222−2−202−200−2i2i−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ232-22-2200-2−2−2220−22002i−2i−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000002-22-2200-2−2−2220−22002i−2i−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ242-22-2200-2−2−2220−22002i−2i−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000002-22-2200-2−2−2220−22002i−2i−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ252-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000002-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ262-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000002-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ274444-4-4-4-4000040000000000000000000000004444-4-4-4-400004000000000000000000000000
χ2844-4-4000022−2222−220002i2−2i2002i−2i2i−2i0000000000000044-4-4000022−2222−220002i2−2i2002i−2i2i−2i00000000000000
χ2944-4-4000022−2222−22000−2i22i200−2i2i−2i2i0000000000000044-4-4000022−2222−22000−2i22i200−2i2i−2i2i00000000000000
χ3044-4-40000−2222−22220002i2−2i200−2i2i−2i2i0000000000000044-4-40000−2222−22220002i2−2i200−2i2i−2i2i00000000000000
χ3144-4-40000−2222−2222000−2i22i2002i−2i2i−2i0000000000000044-4-40000−2222−2222000−2i22i2002i−2i2i−2i00000000000000
χ324-44-4-40042222−22−220−222200000000000000000000004-44-4-40042222−22−220−22220000000000000000000000
χ334-44-4-4004−22−222222022−2200000000000000000000004-44-4-4004−22−222222022−220000000000000000000000
χ344-4-4404-400000000000022−22−2222000000000000004-4-4404-400000000000022−22−222200000000000000
χ354-4-4404-4000000000000−222222−22000000000000004-4-4404-4000000000000−222222−2200000000000000
χ364-4-440-4404-4-4400000000000000000000000004-4-440-4404-4-440000000000000000000000000
χ374-4-440-440-444-400000000000000000000000004-4-440-440-444-40000000000000000000000000
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
χ4622222222-2-2-2-22-2-22222-2-2-2-200000000000000-2-2-2-2-2-2-2-22222-222-2-2-2-2222200000000000000
χ4722222222-2-2-2-22-2-2-2-2-2-2222200000000000000-2-2-2-2-2-2-2-22222-2222222-2-2-2-200000000000000
χ4822222-2-220000-20022-2-2000022−2−222−2−2000000-2-2-2-2-222-20000200-2-2220000−2−222−2−222000000
χ4922222-2-220000-20022-2-20000−2−222−2−222000000-2-2-2-2-222-20000200-2-222000022−2−222−2−2000000
χ5022222-2-220000-200-2-222000022−2−2−2−222000000-2-2-2-2-222-2000020022-2-20000−2−22222−2−2000000
χ5122222-2-220000-200-2-2220000−2−22222−2−2000000-2-2-2-2-222-2000020022-2-2000022−2−2−2−222000000
χ522222-222-22222-2-2-200000000000000002-20000-2-2-2-22-2-22-2-2-2-22220000000000000000-220000
χ532222-222-22222-2-2-20000000000000000-220000-2-2-2-22-2-22-2-2-2-222200000000000000002-20000
χ542222-222-2-2-2-2-2-2220000000000000000002i−2i00-2-2-2-22-2-2222222-2-2000000000000000000−2i2i00
χ552222-222-2-2-2-2-2-222000000000000000000−2i2i00-2-2-2-22-2-2222222-2-20000000000000000002i−2i00
χ562-22-2200-222−2−202−2002i−2ii2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000-22-22-2002−2−2220−2200−2i2i−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ572-22-2200-222−2−202−2002i−2ii2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000-22-22-2002−2−2220−2200−2i2i−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ582-22-2200-222−2−202−200−2i2i−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000-22-22-2002−2−2220−22002i−2ii2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ592-22-2200-222−2−202−200−2i2i−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000-22-22-2002−2−2220−22002i−2ii2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ602-22-2200-2−2−2220−22002i−2i−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000-22-22-200222−2−202−200−2i2ii2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ612-22-2200-2−2−2220−22002i−2i−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000-22-22-200222−2−202−200−2i2ii2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ622-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000-22-22-200222−2−202−2002i−2i−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ632-22-2200-2−2−2220−2200−2i2ii2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000-22-22-200222−2−202−2002i−2i−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ644444-4-4-4-400004000000000000000000000000-4-4-4-444440000-4000000000000000000000000
χ6544-4-4000022−2222−220002i2−2i2002i−2i2i−2i00000000000000-4-4440000−2222−2222000−2i22i200−2i2i−2i2i00000000000000
χ6644-4-4000022−2222−22000−2i22i200−2i2i−2i2i00000000000000-4-4440000−2222−22220002i2−2i2002i−2i2i−2i00000000000000
χ6744-4-40000−2222−22220002i2−2i200−2i2i−2i2i00000000000000-4-444000022−2222−22000−2i22i2002i−2i2i−2i00000000000000
χ6844-4-40000−2222−2222000−2i22i2002i−2i2i−2i00000000000000-4-444000022−2222−220002i2−2i200−2i2i−2i2i00000000000000
χ694-44-4-40042222−22−220−22220000000000000000000000-44-44400-4−22−222222022−220000000000000000000000
χ704-44-4-4004−22−222222022−220000000000000000000000-44-44400-42222−22−220−22220000000000000000000000
χ714-4-4404-400000000000022−22−222200000000000000-444-40-44000000000000−222222−2200000000000000
χ724-4-4404-4000000000000−222222−2200000000000000-444-40-4400000000000022−22−222200000000000000
χ734-4-440-4404-4-440000000000000000000000000-444-404-40-444-40000000000000000000000000
χ744-4-440-440-444-40000000000000000000000000-444-404-404-4-440000000000000000000000000

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