Finite Group Databasebeta

← Group #10827214

Character table — Group #10827214

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222222234444666444444666666121212121212121212121212224444444466661212121212121212121212121212121212124444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-11-11-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ911111-1-1-1-11111111111111-1-111-1-1-1-11111111111111-1-11-1-1-111-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-11-1
χ1011111-1-1-1-11111111111111-1-111-1-1-1-11111111111111-1-11-1-1-111-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-11-11
χ1111111-1-1-1-11111111111111-1-111-1-1-1-1111111111111-111-1-1-11-1-11-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-11-11
χ1211111-1-1-1-11111111111111-1-111-1-1-1-1111111111111-111-1-1-11-1-11-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111-11-1
χ1311111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ1411111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ1511111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-111-1
χ1611111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-11-1-11
χ1722222222222-2-2-2-222222-2-2-2-2222222-2-2-2-22222-2-2-2-200002-2000000000000-2-2000022-2-200000000000000000000
χ1822222222222-2-2-2-2222-2-222-2-2222222-2-2-2-2-2-2-2-222220000-22000000000000-2-20000-2-22200000000000000000000
χ192222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-11111-1-1-1-111110000000000000000
χ212222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1111111112-22-2-2-22-22-2-1-111-1-111-1-1-1-1111111-1-1110000000000000000
χ222222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-111111111-22-22-2-2-22-2211-1-111-1-1-1-111-1-1111111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-122-2-2-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000−i3i3−i3i3−i3i3−i3i311−i3i3−i3i3-1-111−i3i3−i3i30000000000000000
χ242222222222-1-2-2-2-2-1-1-122-2-2-2-2-1-1-1-1-1-11111-1-1-1-1111100002-20000i3−i3i3−i3i3−i3i3−i311i3−i3i3−i3-1-111i3−i3i3−i30000000000000000
χ252222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-111111111-1-1-1-10000-220000−i3i3i3−i3−i3i3i3−i311−i3i3i3−i311-1-1−i3i3i3−i30000000000000000
χ262222222222-1-2-2-2-2-1-1-1-2-222-2-2-1-1-1-1-1-111111111-1-1-1-10000-220000i3−i3−i3i3i3−i3−i3i311i3−i3−i3i311-1-1i3−i3−i3i30000000000000000
χ2722222-2-2-2-222-2-2-2-222222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-20000-22000000000000220000-2-22200000000000000000000
χ2822222-2-2-2-222-2-2-2-2222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2222200002-200000000000022000022-2-200000000000000000000
χ2922222-2-2-2-22-12222-1-1-12222-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-2-22-2-2-222-2-1-11111-1-111-1-111111111-1-10000000000000000
χ3022222-2-2-2-22-12222-1-1-12222-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-222-2-2-22-2-2211-1-1-1-1111111-1-11111-1-1110000000000000000
χ3122222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-11111111122-2-222-2-222-1-1-1-1111111-1-1-1-1-1-1-1-111110000000000000000
χ3222222-2-2-2-22-12222-1-1-1-2-2-2-2-2-2-1-11111-1-1-1-111111111-2-2222222-2-21111-1-1-1-1111111-1-1-1-1-1-1-1-10000000000000000
χ3322222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-111111111-1-1-1-111110000-220000−i3i3i3−i3i3−i3−i3i3-1-1−i3i3i3−i311-1-1i3−i3−i3i30000000000000000
χ3422222-2-2-2-22-1-2-2-2-2-1-1-122-2-222-1-111111111-1-1-1-111110000-220000i3−i3−i3i3−i3i3i3−i3-1-1i3−i3−i3i311-1-1−i3i3i3−i30000000000000000
χ3522222-2-2-2-22-1-2-2-2-2-1-1-1-2-22222-1-1111111111111-1-1-1-100002-20000−i3i3−i3i3i3−i3i3−i3-1-1−i3i3−i3i3-1-111i3−i3i3−i30000000000000000
χ3622222-2-2-2-22-1-2-2-2-2-1-1-1-2-22222-1-1111111111111-1-1-1-100002-20000i3−i3i3−i3−i3i3−i3i3-1-1i3−i3i3−i3-1-111−i3i3−i3i30000000000000000
χ372222-222-2-2-2222-2-222200002-2-2-222-2-222-2-2000000000202000-20-2002200222-200-2-2000000-2-20000000000000000
χ382222-222-2-2-2222-2-222200002-2-2-222-2-222-2-2000000000-20-200020200-2-200-2-22-20022000000220000000000000000
χ392222-222-2-2-22-2-2222220000-22-2-222-2-2-2-22200000000202000-20-2022002200-22-2-2000000-2-2000000000000000000
χ402222-222-2-2-22-2-2222220000-22-2-222-2-2-2-22200000000-20-20002020-2-200-2-200-222200000022000000000000000000
χ412222-222-2-2-2-122-2-2-1-1-100002-211-1-111-1-111−i3−i3i3i3−i3−i3i3i30202000-20-2−i3i3-1-1−i3i3-1-1-11i3−i311−i3i3−i3i3i3−i3110000000000000000
χ422222-222-2-2-2-122-2-2-1-1-100002-211-1-111-1-111−i3−i3i3i3−i3−i3i3i30-20-2000202i3−i311i3−i311-11−i3i3-1-1−i3i3−i3i3−i3i3-1-10000000000000000
χ432222-222-2-2-2-122-2-2-1-1-100002-211-1-111-1-111i3i3−i3−i3i3i3−i3−i30202000-20-2i3−i3-1-1i3−i3-1-1-11−i3i311i3−i3i3−i3−i3i3110000000000000000
χ442222-222-2-2-2-122-2-2-1-1-100002-211-1-111-1-111i3i3−i3−i3i3i3−i3−i30-20-2000202−i3i311−i3i311-11i3−i3-1-1i3−i3i3−i3i3−i3-1-10000000000000000
χ452222-222-2-2-2-1-2-222-1-1-10000-2211-1-11111-1-1−i3−i3i3i3i3i3−i3−i3202000-20-20-1-1−i3i3-1-1−i3i31-111i3−i3−i3i3i3−i311i3−i30000000000000000
χ462222-222-2-2-2-1-2-222-1-1-10000-2211-1-11111-1-1−i3−i3i3i3i3i3−i3−i3-20-2000202011i3−i311i3−i31-1-1-1−i3i3−i3i3i3−i3-1-1−i3i30000000000000000
χ472222-222-2-2-2-1-2-222-1-1-10000-2211-1-11111-1-1i3i3−i3−i3−i3−i3i3i3202000-20-20-1-1i3−i3-1-1i3−i31-111−i3i3i3−i3−i3i311−i3i30000000000000000
χ482222-222-2-2-2-1-2-222-1-1-10000-2211-1-11111-1-1i3i3−i3−i3−i3−i3i3i3-20-2000202011−i3i311−i3i31-1-1-1i3−i3i3−i3−i3i3-1-1i3−i30000000000000000
χ492222-2-2-222-2222-2-22220000-22-2-2-2-22222-2-200000000020-200020-2002200-2-2-2200-2-2000000220000000000000000
χ502222-2-2-222-2222-2-22220000-22-2-2-2-22222-2-2000000000-202000-20200-2-20022-220022000000-2-20000000000000000
χ512222-2-2-222-22-2-22222200002-2-2-2-2-222-2-2220000000020-200020-202200-2-2002-2-2-200000022000000000000000000
χ522222-2-2-222-22-2-22222200002-2-2-2-2-222-2-22200000000-202000-2020-2-20022002-222000000-2-2000000000000000000
χ532222-2-2-222-2-122-2-2-1-1-10000-221111-1-1-1-111−i3−i3i3i3−i3−i3i3i3020-200020-2i3−i3-1-1−i3i3111-1−i3i311i3−i3i3−i3i3−i3-1-10000000000000000
χ542222-2-2-222-2-122-2-2-1-1-10000-221111-1-1-1-111−i3−i3i3i3−i3−i3i3i30-202000-202−i3i311i3−i3-1-11-1i3−i3-1-1i3−i3i3−i3−i3i3110000000000000000
χ552222-2-2-222-2-122-2-2-1-1-10000-221111-1-1-1-111i3i3−i3−i3i3i3−i3−i3020-200020-2−i3i3-1-1i3−i3111-1i3−i311−i3i3−i3i3−i3i3-1-10000000000000000
χ562222-2-2-222-2-122-2-2-1-1-10000-221111-1-1-1-111i3i3−i3−i3i3i3−i3−i30-202000-202i3−i311−i3i3-1-11-1−i3i3-1-1−i3i3−i3i3i3−i3110000000000000000
χ572222-2-2-222-2-1-2-222-1-1-100002-21111-1-111-1-1−i3−i3i3i3i3i3−i3−i320-200020-20-1-1i3−i311−i3i3-1111−i3i3i3−i3−i3i3-1-1i3−i30000000000000000
χ582222-2-2-222-2-1-2-222-1-1-100002-21111-1-111-1-1−i3−i3i3i3i3i3−i3−i3-202000-202011−i3i3-1-1i3−i3-11-1-1i3−i3i3−i3−i3i311−i3i30000000000000000
χ592222-2-2-222-2-1-2-222-1-1-100002-21111-1-111-1-1i3i3−i3−i3−i3−i3i3i320-200020-20-1-1−i3i311i3−i3-1111i3−i3−i3i3i3−i3-1-1−i3i30000000000000000
χ602222-2-2-222-2-1-2-222-1-1-100002-21111-1-111-1-1i3i3−i3−i3−i3−i3i3i3-202000-202011i3−i3-1-1−i3i3-11-1-1−i3i3−i3i3i3−i311i3−i30000000000000000
χ612-2-2220000-222-22-2-22-22i−2i2i−2i002-200002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002i2i−2i−2i002-20000
χ622-2-2220000-222-22-2-22-22i−2i2i−2i002-200002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000−2i−2i2i2i00-220000
χ632-2-2220000-222-22-2-22-2−2i2i−2i2i002-200002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002i2i−2i−2i00-220000
χ642-2-2220000-222-22-2-22-2−2i2i−2i2i002-200002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000−2i−2i2i2i002-20000
χ652-2-2220000-22-22-22-22-22i−2i−2i2i002-20000-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000002i2i−2i−2i00002-2000000
χ662-2-2220000-22-22-22-22-22i−2i−2i2i002-20000-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2i−2i2i2i0000-22000000
χ672-2-2220000-22-22-22-22-2−2i2i2i−2i002-20000-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000002i2i−2i−2i0000-22000000
χ682-2-2220000-22-22-22-22-2−2i2i2i−2i002-20000-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000−2i−2i2i2i00002-2000000
χ6944-4-404-4000400004-4-4000000004-400000000000000000000000000000000000000000000002-22-22-22-200000000
χ7044-4-404-4000400004-4-4000000004-40000000000000000000000000000000000000000000000-22-22-22-2200000000
χ7144-4-40-44000400004-4-400000000-4400000000000000000000000000000000000000000000002-22-2-22-2200000000
χ7244-4-40-44000400004-4-400000000-440000000000000000000000000000000000000000000000-22-222-22-200000000
χ734-44-40004-4040000-4-4400000000004-4000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ744-44-40004-4040000-4-4400000000004-400000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ754-44-4000-44040000-4-440000000000-44000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ764-44-4000-44040000-4-440000000000-4400000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ774-4-4440000-4-24-44-42-224i−4i4i−4i00-220000-22-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ784-4-4440000-4-24-44-42-22−4i4i−4i4i00-220000-22-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ794-4-4440000-4-2-44-442-224i−4i−4i4i00-2200002-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ804-4-4440000-4-2-44-442-22−4i4i4i−4i00-2200002-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ814-4-44-40000444-4-44-44-4000000-4400004-4-4400000000000000000000000000000000000000000000000000000000
χ824-4-44-4000044-444-4-44-4000000-440000-444-400000000000000000000000000000000000000000000000000000000
χ834-4-44-400004-24-4-442-220000002-20000-222-223−23−232323−23−2323000000000000000000000000000000000000000000000000
χ844-4-44-400004-24-4-442-220000002-20000-222-2−232323−23−232323−23000000000000000000000000000000000000000000000000
χ854-4-44-400004-2-444-42-220000002-200002-2-2223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ864-4-44-400004-2-444-42-220000002-200002-2-22−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ8788-8-808-8000-40000-44400000000-4400000000000000000000000000000000000000000000000000000000000000
χ8888-8-80-88000-40000-444000000004-400000000000000000000000000000000000000000000000000000000000000
χ898-88-80008-80-4000044-40000000000-44000000000000000000000000000000000000000000000000000000000000
χ908-88-8000-880-4000044-400000000004-4000000000000000000000000000000000000000000000000000000000000

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