Finite Group Databasebeta

← Group #10830818

Character table — Group #10830818

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order1222222222344446662244446666666666121212121212121222224444446666666612121212121212121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ911111111111-1-1-1-11111111-1-11111111111-1-1-1-111111-11-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-11-11-1
χ1011111111111-1-1-1-11111111-1-11111111111-1-1-1-111111-11-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-11-11
χ1111111111111-1-1-1-11111111-1-11111111111-1-1-1-11111-11-11-1-11-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-11-11
χ1211111111111-1-1-1-11111111-1-11111111111-1-1-1-11111-11-11-1-11-11-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111-11-1
χ1311111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ1411111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1111111-1-1-111-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11-1-11111-1-111-1-111-1-11111-1-11111-1-1-1-1-1-111-111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-11-1-11
χ172222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-2-2-2-2211111111-1-1-1-1-1-1111111110000000000000000
χ192222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-11111-1-1-1-1111122-2-2-222-2-2-2-1-1-1-1111111-1-111-1-1-1-111110000000000000000
χ202222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-11111-1-1-1-11111-2-222-2-2-222-21111-1-1-1-111-1-1111111-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-11111-1-1-1-12-22-2-22-22-2-2-1-111-1-111111111-1-111-1-1110000000000000000
χ222222222222-1-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-22-22-2-22-22-211-1-111-1-111111111-1-111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111112-2-2222-2-222-1-11111-1-1-1-111-1-1-1-11111-1-10000000000000000
χ242222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1111111111111-222-22-222-2211-1-1-1-111-1-111-1-111-1-1-1-1110000000000000000
χ2522222-2-2-22-2222-2-222200002-222-2-2-2-2000022-2-200000022000-2-2000002222002-2000000-2-2-2-20000000000000000
χ2622222-2-2-22-2222-2-222200002-222-2-2-2-2000022-2-2000000-2-20002200000-2-2-2-2002-200000022220000000000000000
χ2722222-2-2-22-22-2-2222220000-2222-2-2-2-20000-2-2220000002-2000-220000022-2-200-22000000-2-2220000000000000000
χ2822222-2-2-22-22-2-2222220000-2222-2-2-2-20000-2-222000000-220002-200000-2-22200-2200000022-2-20000000000000000
χ2922222-2-2-22-2-122-2-2-1-1-100002-2-1-11111−i3−i3i3i3-1-111−i3−i3i3i30022000-2-20−i3i3−i3i3-1-1-1-1−i3i3-11−i3i3−i3i3−i3i311110000000000000000
χ3022222-2-2-22-2-122-2-2-1-1-100002-2-1-11111−i3−i3i3i3-1-111−i3−i3i3i300-2-2000220i3−i3i3−i31111−i3i3-11−i3i3i3−i3i3−i3-1-1-1-10000000000000000
χ3122222-2-2-22-2-122-2-2-1-1-100002-2-1-11111i3i3−i3−i3-1-111i3i3−i3−i30022000-2-20i3−i3i3−i3-1-1-1-1i3−i3-11i3−i3i3−i3i3−i311110000000000000000
χ3222222-2-2-22-2-122-2-2-1-1-100002-2-1-11111i3i3−i3−i3-1-111i3i3−i3−i300-2-2000220−i3i3−i3i31111i3−i3-11i3−i3−i3i3−i3i3-1-1-1-10000000000000000
χ3322222-2-2-22-2-1-2-222-1-1-10000-22-1-11111−i3−i3i3i311-1-1−i3−i3i3i3002-2000-220−i3i3i3−i3-1-111i3−i31-1i3−i3−i3i3i3−i311-1-10000000000000000
χ3422222-2-2-22-2-1-2-222-1-1-10000-22-1-11111−i3−i3i3i311-1-1−i3−i3i3i300-220002-20i3−i3−i3i311-1-1i3−i31-1i3−i3i3−i3−i3i3-1-1110000000000000000
χ3522222-2-2-22-2-1-2-222-1-1-10000-22-1-11111i3i3−i3−i311-1-1i3i3−i3−i3002-2000-220i3−i3−i3i3-1-111−i3i31-1−i3i3i3−i3−i3i311-1-10000000000000000
χ3622222-2-2-22-2-1-2-222-1-1-10000-22-1-11111i3i3−i3−i311-1-1i3i3−i3−i300-220002-20−i3i3i3−i311-1-1−i3i31-1−i3i3−i3i3i3−i3-1-1110000000000000000
χ372222-22-2-2-22222-2-22220000-22-2-222-2-2000022-2-2000022000-2-20002222000000-2200-2-2-2-200000000000000000000
χ382222-22-2-2-22222-2-22220000-22-2-222-2-2000022-2-20000-2-200022000-2-2-2-2000000-2200222200000000000000000000
χ392222-22-2-2-222-2-22222200002-2-2-222-2-20000-2-22200002-2000-2200022-2-20000002-200-2-22200000000000000000000
χ402222-22-2-2-222-2-22222200002-2-2-222-2-20000-2-2220000-220002-2000-2-2220000002-20022-2-200000000000000000000
χ412222-22-2-2-22-122-2-2-1-1-10000-2211-1-111−i3−i3i3i3-1-111i3i3−i3−i322000-2-2000-1-1-1-1−i3i3−i3i3i3−i31-1−i3i31111−i3i3−i3i30000000000000000
χ422222-22-2-2-22-122-2-2-1-1-10000-2211-1-111−i3−i3i3i3-1-111i3i3−i3−i3-2-2000220001111i3−i3i3−i3i3−i31-1−i3i3-1-1-1-1i3−i3i3−i30000000000000000
χ432222-22-2-2-22-122-2-2-1-1-10000-2211-1-111i3i3−i3−i3-1-111−i3−i3i3i322000-2-2000-1-1-1-1i3−i3i3−i3−i3i31-1i3−i31111i3−i3i3−i30000000000000000
χ442222-22-2-2-22-122-2-2-1-1-10000-2211-1-111i3i3−i3−i3-1-111−i3−i3i3i3-2-2000220001111−i3i3−i3i3−i3i31-1i3−i3-1-1-1-1−i3i3−i3i30000000000000000
χ452222-22-2-2-22-1-2-222-1-1-100002-211-1-111−i3−i3i3i311-1-1i3i3−i3−i32-2000-22000-1-111−i3i3i3−i3−i3i3-11i3−i311-1-1−i3i3i3−i30000000000000000
χ462222-22-2-2-22-1-2-222-1-1-100002-211-1-111−i3−i3i3i311-1-1i3i3−i3−i3-220002-200011-1-1i3−i3−i3i3−i3i3-11i3−i3-1-111i3−i3−i3i30000000000000000
χ472222-22-2-2-22-1-2-222-1-1-100002-211-1-111i3i3−i3−i311-1-1−i3−i3i3i32-2000-22000-1-111i3−i3−i3i3i3−i3-11−i3i311-1-1i3−i3−i3i30000000000000000
χ482222-22-2-2-22-1-2-222-1-1-100002-211-1-111i3i3−i3−i311-1-1−i3−i3i3i3-220002-200011-1-1−i3i3i3−i3i3−i3-11−i3i3-1-111−i3i3i3−i30000000000000000
χ492222-2-222-2-22222222222-2-2-2-2-2-2-2-22222222222-2-2-2-20000-20000200000000-2-2-2-222000000000000000000000000
χ502222-2-222-2-222222222-2-222-2-2-2-2-2-222-2-2-2-222222222000020000-20000000022-2-2-2-2000000000000000000000000
χ512222-2-222-2-22-2-2-2-222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2000020000-2000000002222-2-2000000000000000000000000
χ522222-2-222-2-22-2-2-2-2222-2-22222-2-2-2-222-2-2-2-2-2-2-2-222220000-20000200000000-2-22222000000000000000000000000
χ532222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-111110000-200002−i3i3−i3i3−i3i3−i3i31111-1-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ542222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-1-1-1-1-111110000-200002i3−i3i3−i3i3−i3i3−i31111-1-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ552222-2-222-2-2-12222-1-1-1-2-222-2-21111-1-11111-1-1-1-1-1-1-1-1000020000-2−i3i3−i3i3i3−i3i3−i3-1-11111i3−i3i3−i3−i3i3−i3i30000000000000000
χ562222-2-222-2-2-12222-1-1-1-2-222-2-21111-1-11111-1-1-1-1-1-1-1-1000020000-2i3−i3i3−i3−i3i3−i3i3-1-11111−i3i3−i3i3i3−i3i3−i30000000000000000
χ572222-2-222-2-2-1-2-2-2-2-1-1-122-2-2221111-1-1-1-1-1-111111111000020000-2−i3i3i3−i3−i3i3i3−i3-1-1-1-111i3−i3−i3i3i3−i3−i3i30000000000000000
χ582222-2-222-2-2-1-2-2-2-2-1-1-122-2-2221111-1-1-1-1-1-111111111000020000-2i3−i3−i3i3i3−i3−i3i3-1-1-1-111−i3i3i3−i3−i3i3i3−i30000000000000000
χ592222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-111111111-1-1-1-10000-200002−i3i3i3−i3i3−i3−i3i311-1-1-1-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-111111111-1-1-1-10000-200002i3−i3−i3i3−i3i3i3−i311-1-1-1-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ612-22-2222-2-2-220000-2-222-22-2002-22-22-22-22-200002-22-20000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ622-22-2222-2-2-220000-2-222-22-2002-22-22-22-22-200002-22-2000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ632-22-2222-2-2-220000-2-22-22-22002-22-22-2-22-220000-22-220000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ642-22-2222-2-2-220000-2-22-22-22002-22-22-2-22-220000-22-22000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ652-22-2-2-22-22220000-2-222-2-2200-22-222-22-22-20000-22-220000000000000000000000000000000022-2-200002-2000000
χ662-22-2-2-22-22220000-2-222-2-2200-22-222-22-22-20000-22-2200000000000000000000000000000000-2-2220000-22000000
χ672-22-2-2-22-22220000-2-22-222-200-22-222-2-22-2200002-22-20000000000000000000000000000000022-2-20000-22000000
χ682-22-2-2-22-22220000-2-22-222-200-22-222-2-22-2200002-22-200000000000000000000000000000000-2-22200002-2000000
χ6944-4-40000004004i−4i4-4-40000000000000000004i−4i0000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ7044-4-40000004004i−4i4-4-40000000000000000004i−4i000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ7144-4-4000000400−4i4i4-4-4000000000000000000−4i4i0000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ7244-4-4000000400−4i4i4-4-4000000000000000000−4i4i000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ734-44-4444-4-4-4-2000022-24-44-400-22-22-22-22-220000-22-22000000000000000000000000000000000000000000000000
χ744-44-4444-4-4-4-2000022-2-44-4400-22-22-222-22-200002-22-2000000000000000000000000000000000000000000000000
χ754-44-44-4-44-4440000-4-440000004-4-44-44000000000000000000000000000000000000000000000000000000000000
χ764-44-44-4-44-44-2000022-2000000-222-22-2−2i32i32i3−2i30000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ774-44-44-4-44-44-2000022-2000000-222-22-22i3−2i3−2i32i300002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ784-44-4-44-444-440000-4-44000000-444-4-44000000000000000000000000000000000000000000000000000000000000
χ794-44-4-44-444-4-2000022-20000002-2-222-2−2i32i32i3−2i300002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ804-44-4-44-444-4-2000022-20000002-2-222-22i3−2i3−2i32i30000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ814-44-4-4-44-444-2000022-24-4-44002-22-2-22-22-2200002-22-2000000000000000000000000000000000000000000000000
χ824-44-4-4-44-444-2000022-2-444-4002-22-2-222-22-20000-22-22000000000000000000000000000000000000000000000000
χ834-4-4400000044-400-44-400000000000000004-4000000000000000000000000000000000000002-2-222-2-2200000000
χ844-4-4400000044-400-44-400000000000000004-400000000000000000000000000000000000000-222-2-222-200000000
χ854-4-440000004-4400-44-40000000000000000-44000000000000000000000000000000000000002-2-22-222-200000000
χ864-4-440000004-4400-44-40000000000000000-4400000000000000000000000000000000000000-222-22-2-2200000000
χ8788-8-8000000-4008i−8i-444000000000000000000−4i4i0000000000000000000000000000000000000000000000000000
χ8888-8-8000000-400−8i8i-4440000000000000000004i−4i0000000000000000000000000000000000000000000000000000
χ898-8-88000000-48-8004-440000000000000000-44000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4-88004-4400000000000000004-4000000000000000000000000000000000000000000000000000000

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