Finite Group Databasebeta

← Group #10822722

Character table — Group #10822722

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222222222344444444666666666661212121212121212222244444444666666661212121212121212121212121212121288888888444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-11-1-1-11-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-11-1-1-11-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11-1111-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2002-200-220000000022-2-2000000000000-2-22200000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200-22002-200000000-2-22200000000000022-2-200000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-1111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-1-1-1111111111111-1-1-1-100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-200-220000−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311-1-100000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-200-220000i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311-1-100000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22002-20000−i3−i3i3i311-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-1-11100000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22002-20000i3i3−i3−i311-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-1-11100000000000000000000
χ2722222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-22222002200-2-2000000002222000000000000-2-2-2-200000000000000000000
χ2822222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-2222200-2-2002200000000-2-2-2-2000000000000222200000000000000000000
χ2922222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111222-2-2-22-222-2-2-1-1-1-1-1-111-1-1-1-111111111-1-11100000000000000000000
χ3022222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-1111122-22-2-2-22-2-222-1-1-1-111-1-11111-1-1-1-1111111-1-100000000000000000000
χ3122222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2-22-2222-2-2-2221111-1-1111111-1-1-1-1-1-1-1-1-1-11100000000000000000000
χ3222222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2222-2222-2-2111111-1-1-1-1-1-11111-1-1-1-111-1-100000000000000000000
χ3322222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1002200-2-20000−i3−i3i3i3-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3111100000000000000000000
χ3422222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-1002200-2-20000i3i3−i3−i3-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3111100000000000000000000
χ3522222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100-2-200220000−i3−i3i3i31111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-1-1-100000000000000000000
χ3622222222-2-2-2-2-1-2-22222-2-2-1-1-1-1-1-1-111111111-1-1-1-100-2-200220000i3i3−i3−i31111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-1-1-100000000000000000000
χ37222-22-2-2-222-2-222-222-2-22-222-2-2-2-2222-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ38222-22-2-2-222-2-222-222-2-22-222-2-2-2-2222-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ39222-22-2-2-222-2-22-22-2-222-2222-2-2-2-2222-2-2-2-222-2-222000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ40222-22-2-2-222-2-22-22-2-222-2222-2-2-2-2222-2-2-2-222-2-22200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ41222-22-2-2-2-2-22222-2-2-2222-222-2-2-2-22-2-22222-2-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ42222-22-2-2-2-2-22222-2-2-2222-222-2-2-2-22-2-22222-2-2-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ43222-22-2-2-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-22222-2-2000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ44222-22-2-2-2-2-2222-2222-2-2-2222-2-2-2-22-2-222-2-22222-2-200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ452-2-222-2-222-22-22222-22-2-2-2-2-222-2-222-22-22-22-22-22-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ462-2-222-2-222-22-22222-22-2-2-2-2-222-2-222-22-22-22-22-22-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ472-2-222-2-222-22-22-2-2-22-2222-2-222-2-222-22-2-22-22-22-2200000000000000000000000000000000000000000000000000002-22-2
χ482-2-222-2-222-22-22-2-2-22-2222-2-222-2-222-22-2-22-22-22-220000000000000000000000000000000000000000000000000000-22-22
χ492-2-222-2-22-22-22222-22-22-2-2-2-222-2-22-22-222-22-2-22-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ502-2-222-2-22-22-22222-22-22-2-2-2-222-2-22-22-222-22-2-22-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ512-2-222-2-22-22-222-2-22-22-222-2-222-2-22-22-22-22-222-22-200000000000000000000000000000000000000000000000000002-2-22
χ522-2-222-2-22-22-222-2-22-22-222-2-222-2-22-22-22-22-222-22-20000000000000000000000000000000000000000000000000000-222-2
χ532-2-2-2222-22-2-2222-22-2-22-22-2-2-2-22222-2-222-2-222-2-22000000002-22-2000000002-22-22-22-20000000000000000000000000000
χ542-2-2-2222-22-2-2222-22-2-22-22-2-2-2-22222-2-222-2-222-2-2200000000-22-2200000000-22-22-22-220000000000000000000000000000
χ552-2-2-2222-22-2-222-22-222-22-2-2-2-2-22222-2-22-222-2-222-22-2002-20000002-22-20000000000002-22-2000000000000000000000000
χ562-2-2-2222-22-2-222-22-222-22-2-2-2-2-22222-2-22-222-2-222-2-2200-22000000-22-22000000000000-22-22000000000000000000000000
χ572-2-2-2222-22-2-22-12-22-2-22-221111-1-1-1-111-1-111-1-111-1000000002-22-2−i3i3i3−i3−i3i3−i3i3-11-11-11-11−i3i3i3−i3−i3i3−i3i300000000000000000000
χ582-2-2-2222-22-2-22-12-22-2-22-221111-1-1-1-111-1-111-1-111-1000000002-22-2i3−i3−i3i3i3−i3i3−i3-11-11-11-11i3−i3−i3i3i3−i3i3−i300000000000000000000
χ592-2-2-2222-22-2-22-12-22-2-22-221111-1-1-1-111-1-111-1-111-100000000-22-22−i3i3i3−i3i3−i3i3−i31-11-11-11-1−i3i3i3−i3i3−i3i3−i300000000000000000000
χ602-2-2-2222-22-2-22-12-22-2-22-221111-1-1-1-111-1-111-1-111-100000000-22-22i3−i3−i3i3−i3i3−i3i31-11-11-11-1i3−i3−i3i3−i3i3−i3i300000000000000000000
χ612-2-2-2222-22-2-22-1-22-222-22-21111-1-1-1-111-11-1-111-1-112-2002-2000000-11-11−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-11-11i3−i3−i3i300000000000000000000
χ622-2-2-2222-22-2-22-1-22-222-22-21111-1-1-1-111-11-1-111-1-112-2002-2000000-11-11i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-11-11−i3i3i3−i300000000000000000000
χ632-2-2-2222-22-2-22-1-22-222-22-21111-1-1-1-111-11-1-111-1-11-2200-220000001-11-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-11-1i3−i3−i3i300000000000000000000
χ642-2-2-2222-22-2-22-1-22-222-22-21111-1-1-1-111-11-1-111-1-11-2200-220000001-11-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-11-1−i3i3i3−i300000000000000000000
χ652-2-2-2222-2-222-222-2-222-2-22-2-2-2-2222-222-22-2-22-222-2000000002-2-22000000002-22-2-22-220000000000000000000000000000
χ662-2-2-2222-2-222-222-2-222-2-22-2-2-2-2222-222-22-2-22-222-200000000-222-200000000-22-222-22-20000000000000000000000000000
χ672-2-2-2222-2-222-22-222-2-222-2-2-2-2-2222-222-2-222-22-2-222-200-220000002-22-2000000000000-22-22000000000000000000000000
χ682-2-2-2222-2-222-22-222-2-222-2-2-2-2-2222-222-2-222-22-2-22-22002-2000000-22-220000000000002-22-2000000000000000000000000
χ692-2-2-2222-2-222-2-12-2-222-2-221111-1-1-11-1-11-111-11-1-11000000002-2-22−i3i3i3−i3−i3i3i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i300000000000000000000
χ702-2-2-2222-2-222-2-12-2-222-2-221111-1-1-11-1-11-111-11-1-11000000002-2-22i3−i3−i3i3i3−i3−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i300000000000000000000
χ712-2-2-2222-2-222-2-12-2-222-2-221111-1-1-11-1-11-111-11-1-1100000000-222-2−i3i3i3−i3i3−i3−i3i31-11-1-11-11i3−i3−i3i3i3−i3−i3i300000000000000000000
χ722-2-2-2222-2-222-2-12-2-222-2-221111-1-1-11-1-11-111-11-1-1100000000-222-2i3−i3−i3i3−i3i3i3−i31-11-1-11-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ732-2-2-2222-2-222-2-1-222-2-222-21111-1-1-11-1-111-1-11-111-12-200-22000000-11-11−i3i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1i3−i3i3−i300000000000000000000
χ742-2-2-2222-2-222-2-1-222-2-222-21111-1-1-11-1-111-1-11-111-12-200-22000000-11-11i3−i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1−i3i3−i3i300000000000000000000
χ752-2-2-2222-2-222-2-1-222-2-222-21111-1-1-11-1-111-1-11-111-1-22002-20000001-11-1−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-11i3−i3i3−i300000000000000000000
χ762-2-2-2222-2-222-2-1-222-2-222-21111-1-1-11-1-111-1-11-111-1-22002-20000001-11-1i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-11−i3i3−i3i300000000000000000000
χ77444-44-4-4-444-4-4-24-444-4-44-4-2-22222-2-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ78444-44-4-4-444-4-4-2-44-4-444-44-2-22222-2-2-22222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-4-4-444-24-4-4-4444-4-2-22222-222-2-2-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-4-444-2-4444-4-4-44-2-22222-222-2-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ8144-44-44-4-400004000000004-44-44-4-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ8244-44-44-4-400004000000004-44-44-4-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ8344-4-4-4-44400004000000004-4-44-44-4000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ8444-4-4-4-44400004000000004-4-44-44-40000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ854-444-4-44-40000400000000-444-4-44-4000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ864-444-4-44-40000400000000-444-4-44-40000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ874-44-4-44-440000400000000-44-444-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ884-44-4-44-440000400000000-44-444-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ894-4-444-4-444-44-4-2444-44-4-4-422-2-222-2-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ904-4-444-4-444-44-4-2-4-4-44-444422-2-222-2-22-222-22-22-22-200000000000000000000000000000000000000000000000000000000
χ914-4-444-4-44-44-44-244-44-44-4-422-2-222-22-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ924-4-444-4-44-44-44-2-4-44-44-44422-2-222-22-22-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ9388-88-88-8-80000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-8-8880000-400000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-8-88-80000-4000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-880000-4000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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