Finite Group Databasebeta

← Group #10850463

Character table — Group #10850463

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222224444444444444444444444444888888888888888888888888888888882424242424242424242424244848
order1222222222344666224444466666666661212121212121212222244444466666666121212121212121212121212121222224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111-1-1111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111-1-1111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111-1-1111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111-1-1111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ911111111111-1-111111-1-1-1111111111111-1-1-1-111111-11-1-1-11-11-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-11-1
χ1011111111111-1-111111-1-1-1111111111111-1-1-1-111111-11-1-1-11-11-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-11
χ1111111111111-1-111111-1-1-1111111111111-1-1-1-11111-11-11-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1111-1
χ1211111111111-1-111111-1-1-1111111111111-1-1-1-11111-11-11-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-11
χ1311111111111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-111-11
χ1411111111111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11111-1-11-1
χ1511111111111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-11111-1-111-1-111-1-11111-1-111-1-1-1-11111-1-1-11
χ1611111111111-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111-1
χ172222222222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ182222222222-122-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-1-1-11111111100000000000000
χ192222222222-122-1-1-1-2-2222-2-2-1-1-1-1-1-11111-1-1-1-1111122-2-2-2-222-2-2-1-1-1-1111111-1-111-1-1-1-1111100000000000000
χ202222222222-122-1-1-1-2-2222-2-2-1-1-1-1-1-11111-1-1-1-11111-2-222-2-2-2-2221111-1-1-1-111-1-1111111-1-1-1-100000000000000
χ212222222222-1-2-2-1-1-122-2-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-12-22-2-2-22-22-2-1-111-1-111111111-1-111-1-11100000000000000
χ222222222222-1-2-2-1-1-122-2-2-222-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-22-22-2-2-22-2211-1-111-1-111111111-1-111-1-100000000000000
χ232222222222-1-2-2-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-11111111111112-2-22222-2-22-1-11111-1-1-1-111-1-1-1-11111-1-100000000000000
χ242222222222-1-2-2-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111-222-222-222-211-1-1-1-111-1-111-1-111-1-1-1-11100000000000000
χ2522222-2-2-2-22222222222-2-2-2-222-2-2-2-222222222-2-2-2-20000-22000000000000-2-2-2-2220000000000000000000000
χ2622222-2-2-2-22222222-2-22-2-22222-2-2-2-2-2-2-2-22222222200002-200000000000022-2-2-2-20000000000000000000000
χ2722222-2-2-2-222-2-222222-222-2-222-2-2-2-22222-2-2-2-2-2-2-2-200002-20000000000002222-2-20000000000000000000000
χ2822222-2-2-2-222-2-2222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222220000-22000000000000-2-222220000000000000000000000
χ2922222-2-2-2-22-122-1-1-1222-2-2-2-2-1-11111-1-1-1-1-1-1-1-111110000-220000−i3i3−i3i3−i3i3−i3i31111-1-1−i3i3−i3i3−i3i3−i3i300000000000000
χ3022222-2-2-2-22-122-1-1-1222-2-2-2-2-1-11111-1-1-1-1-1-1-1-111110000-220000i3−i3i3−i3i3−i3i3−i31111-1-1i3−i3i3−i3i3−i3i3−i300000000000000
χ3122222-2-2-2-22-122-1-1-1-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100002-20000−i3i3−i3i3i3−i3i3−i3-1-11111−i3i3−i3i3i3−i3i3−i300000000000000
χ3222222-2-2-2-22-122-1-1-1-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100002-20000i3−i3i3−i3−i3i3−i3i3-1-11111i3−i3i3−i3−i3i3−i3i300000000000000
χ3322222-2-2-2-22-1-2-2-1-1-122-222-2-2-1-11111-1-1-1-11111111100002-20000−i3i3i3−i3−i3i3i3−i3-1-1-1-111−i3i3i3−i3−i3i3i3−i300000000000000
χ3422222-2-2-2-22-1-2-2-1-1-122-222-2-2-1-11111-1-1-1-11111111100002-20000i3−i3−i3i3i3−i3−i3i3-1-1-1-111i3−i3−i3i3i3−i3−i3i300000000000000
χ3522222-2-2-2-22-1-2-2-1-1-1-2-2-22222-1-1111111111111-1-1-1-10000-220000−i3i3i3−i3i3−i3−i3i311-1-1-1-1−i3i3i3−i3i3−i3−i3i300000000000000
χ3622222-2-2-2-22-1-2-2-1-1-1-2-2-22222-1-1111111111111-1-1-1-10000-220000i3−i3−i3i3−i3i3i3−i311-1-1-1-1i3−i3−i3i3−i3i3i3−i300000000000000
χ372222-222-2-2-222222200-22-200-2-222-2-2000022-2-2000000220000-2-200002222002-2000000-2-2-2-200000000000000
χ382222-222-2-2-222222200-22-200-2-222-2-2000022-2-2000000-2-20000220000-2-2-2-2002-2000000222200000000000000
χ392222-222-2-2-22-2-2222002-2200-2-222-2-20000-2-2220000002-20000-22000022-2-200-22000000-2-22200000000000000
χ402222-222-2-2-22-2-2222002-2200-2-222-2-20000-2-222000000-2200002-20000-2-22200-2200000022-2-200000000000000
χ412222-222-2-2-2-122-1-1-100-22-20011-1-111−i3−i3i3i3-1-111−i3−i3i3i300220000-2-2−i3i3−i3i3-1-1-1-1−i3i3-11−i3i3i3−i3i3−i3111100000000000000
χ422222-222-2-2-2-122-1-1-100-22-20011-1-111−i3−i3i3i3-1-111−i3−i3i3i300-2-2000022i3−i3i3−i31111−i3i3-11−i3i3−i3i3−i3i3-1-1-1-100000000000000
χ432222-222-2-2-2-122-1-1-100-22-20011-1-111i3i3−i3−i3-1-111i3i3−i3−i300220000-2-2i3−i3i3−i3-1-1-1-1i3−i3-11i3−i3−i3i3−i3i3111100000000000000
χ442222-222-2-2-2-122-1-1-100-22-20011-1-111i3i3−i3−i3-1-111i3i3−i3−i300-2-2000022−i3i3−i3i31111i3−i3-11i3−i3i3−i3i3−i3-1-1-1-100000000000000
χ452222-222-2-2-2-1-2-2-1-1-1002-220011-1-111−i3−i3i3i311-1-1−i3−i3i3i3002-20000-22−i3i3i3−i3-1-111i3−i31-1i3−i3i3−i3−i3i311-1-100000000000000
χ462222-222-2-2-2-1-2-2-1-1-1002-220011-1-111−i3−i3i3i311-1-1−i3−i3i3i300-2200002-2i3−i3−i3i311-1-1i3−i31-1i3−i3−i3i3i3−i3-1-11100000000000000
χ472222-222-2-2-2-1-2-2-1-1-1002-220011-1-111i3i3−i3−i311-1-1i3i3−i3−i3002-20000-22i3−i3−i3i3-1-111−i3i31-1−i3i3−i3i3i3−i311-1-100000000000000
χ482222-222-2-2-2-1-2-2-1-1-1002-220011-1-111i3i3−i3−i311-1-1i3i3−i3−i300-2200002-2−i3i3i3−i311-1-1−i3i31-1−i3i3i3−i3−i3i3-1-11100000000000000
χ492222-2-2-222-222222200-2-2200-2-2-2-222000022-2-20000220000-2-2002222000000-2200-2-2-2-2000000000000000000
χ502222-2-2-222-222222200-2-2200-2-2-2-222000022-2-20000-2-200002200-2-2-2-2000000-22002222000000000000000000
χ512222-2-2-222-22-2-22220022-200-2-2-2-2220000-2-22200002-20000-220022-2-20000002-200-2-222000000000000000000
χ522222-2-2-222-22-2-22220022-200-2-2-2-2220000-2-2220000-2200002-200-2-2220000002-20022-2-2000000000000000000
χ532222-2-2-222-2-122-1-1-100-2-22001111-1-1−i3−i3i3i3-1-111i3i3−i3−i3220000-2-200-1-1-1-1−i3i3−i3i3i3−i31-1−i3i31111i3−i3i3−i300000000000000
χ542222-2-2-222-2-122-1-1-100-2-22001111-1-1−i3−i3i3i3-1-111i3i3−i3−i3-2-2000022001111i3−i3i3−i3i3−i31-1−i3i3-1-1-1-1−i3i3−i3i300000000000000
χ552222-2-2-222-2-122-1-1-100-2-22001111-1-1i3i3−i3−i3-1-111−i3−i3i3i3220000-2-200-1-1-1-1i3−i3i3−i3−i3i31-1i3−i31111−i3i3−i3i300000000000000
χ562222-2-2-222-2-122-1-1-100-2-22001111-1-1i3i3−i3−i3-1-111−i3−i3i3i3-2-2000022001111−i3i3−i3i3−i3i31-1i3−i3-1-1-1-1i3−i3i3−i300000000000000
χ572222-2-2-222-2-1-2-2-1-1-10022-2001111-1-1−i3−i3i3i311-1-1i3i3−i3−i32-20000-2200-1-111−i3i3i3−i3−i3i3-11i3−i311-1-1i3−i3−i3i300000000000000
χ582222-2-2-222-2-1-2-2-1-1-10022-2001111-1-1−i3−i3i3i311-1-1i3i3−i3−i3-2200002-20011-1-1i3−i3−i3i3−i3i3-11i3−i3-1-111−i3i3i3−i300000000000000
χ592222-2-2-222-2-1-2-2-1-1-10022-2001111-1-1i3i3−i3−i311-1-1−i3−i3i3i32-20000-2200-1-111i3−i3−i3i3i3−i3-11−i3i311-1-1−i3i3i3−i300000000000000
χ602222-2-2-222-2-1-2-2-1-1-10022-2001111-1-1i3i3−i3−i311-1-1−i3−i3i3i3-2200002-20011-1-1−i3i3i3−i3i3−i3-11−i3i3-1-111i3−i3−i3i300000000000000
χ612-2-22-22-22-22200-2-222-20002-22-22-22-22-22-200002-22-2000000000000000000000000000000000000002-2002-200
χ622-2-22-22-22-22200-2-222-20002-22-22-22-22-22-200002-22-200000000000000000000000000000000000000-2200-2200
χ632-2-22-22-22-22200-2-22-22000-222-22-22-2-22-220000-22-22000000000000000000000000000000000000002-200-2200
χ642-2-22-22-22-22200-2-22-22000-222-22-22-2-22-220000-22-2200000000000000000000000000000000000000-22002-200
χ652-2-22-2-22-222200-2-222-2000-222-2-22-222-22-20000-22-220000000000000000000000000000000000002-2002-20000
χ662-2-22-2-22-222200-2-222-2000-222-2-22-222-22-20000-22-22000000000000000000000000000000000000-2200-220000
χ672-2-22-2-22-222200-2-22-220002-22-2-22-22-22-2200002-22-20000000000000000000000000000000000002-200-220000
χ682-2-22-2-22-222200-2-22-220002-22-2-22-22-22-2200002-22-2000000000000000000000000000000000000-22002-20000
χ694-44-400000044-4-44-4000000000000000004-4000000000000000000000000000000000000002-22-20000000000
χ704-44-400000044-4-44-4000000000000000004-400000000000000000000000000000000000000-22-220000000000
χ714-44-40000004-44-44-400000000000000000-44000000000000000000000000000000000000002-2-220000000000
χ724-44-40000004-44-44-400000000000000000-4400000000000000000000000000000000000000-222-20000000000
χ734-4-4444-4-44-4400-4-440000000-444-4-440000000000000000000000000000000000000000000000000000000000
χ744-4-4444-4-44-4-20022-200000002-2-222-2−2i32i32i3−2i30000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ754-4-4444-4-44-4-20022-200000002-2-222-22i3−2i3−2i32i300002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ764-4-444-444-4-4400-4-440000000-44-444-40000000000000000000000000000000000000000000000000000000000
χ774-4-444-444-4-4-20022-200000002-22-2-22−2i32i32i3−2i300002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-4-444-444-4-4-20022-200000002-22-2-222i3−2i3−2i32i30000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ794-4-44-44-44-44-20022-24-40004-4-22-22-22-22-220000-22-220000000000000000000000000000000000000000000000
χ804-4-44-44-44-44-20022-2-44000-44-22-22-222-22-200002-22-20000000000000000000000000000000000000000000000
χ814-4-44-4-44-444-20022-24-4000-44-222-22-2-22-2200002-22-20000000000000000000000000000000000000000000000
χ824-4-44-4-44-444-20022-2-440004-4-222-22-22-22-20000-22-220000000000000000000000000000000000000000000000
χ8388-8-80000008008-8-800000000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8000000-400-444000000000000000000043−4300000000000000000000000000000000000000000000000000
χ8588-8-8000000-400-4440000000000000000000−434300000000000000000000000000000000000000000000000000
χ868-88-8000000-48-84-4400000000000000000-440000000000000000000000000000000000000000000000000000
χ878-88-8000000-4-884-44000000000000000004-40000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).