Finite Group Databasebeta

← Group #10702687

Character table — Group #10702687

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122244442222223444444666121212126666661212121212122244666688888888121212122424242424242424242424242424242488888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-11111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-11111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-11111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−iiiii−i−i−i−iii
χ121111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-11111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiii−i−i−i−iiiii−i−i
χ131111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iii−i−i−i−iii−i−iii
χ141111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−iiiii−i−iii−i−i
χ151111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-1111-111-1111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i−i−iii
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222-2-2-2-22-2-22-2-22222222222-2-2-2-2-2-222-2-22-22-222-2-20000000022-2-2000000000000000000000000000000000000
χ222222222222-2-2-2-22-2-22-2-22222222222-2-2-2-2-2-222-2-2-22-22-2-22200000000-2-222000000000000000000000000000000000000
χ232222222222-2-2-2-2-1-2-22-2-22-1-1-1-1-1-1-1-1-1111111-1-1112-22-2-1-11100000000-1-11133−3−333−3−333−3−333−3−300000000000000000000
χ242222222222-2-2-2-2-1-2-22-2-22-1-1-1-1-1-1-1-1-1111111-1-1112-22-2-1-11100000000-1-111−3−333−3−333−3−333−3−33300000000000000000000
χ252222222222-2-2-2-2-1-2-22-2-22-1-1-1-1-1-1-1-1-1111111-1-111-22-2211-1-10000000011-1-133−3−333−3−3−3−333−3−33300000000000000000000
χ262222222222-2-2-2-2-1-2-22-2-22-1-1-1-1-1-1-1-1-1111111-1-111-22-2211-1-10000000011-1-1−3−333−3−33333−3−333−3−300000000000000000000
χ2722222222-2-222-2-222-2-22-2-22222222-2-222-2-22-2-2-22-200000000000000000000000000000000000000000000000000002-22-2
χ2822222222-2-222-2-222-2-22-2-22222222-2-222-2-22-2-2-22-20000000000000000000000000000000000000000000000000000-22-22
χ2922222222-2-2-2-2222-22-2-22-22222222-2-2-2-222-22-2-2-22000000000000000000000000000000000000000000002-22-200000000
χ3022222222-2-2-2-2222-22-2-22-22222222-2-2-2-222-22-2-2-2200000000000000000000000000000000000000000000-22-2200000000
χ312222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-22-2-2222-2-200000000-2-222000000000000000000000000000000000000
χ322222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-222-2-2-2220000000022-2-2000000000000000000000000000000000000
χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-2-22-1-1110000000011-1-133−3−3−3−33333−3−3−3−33300000000000000000000
χ342222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-2-22-1-1110000000011-1-1−3−33333−3−3−3−33333−3−300000000000000000000
χ352222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-222-211-1-100000000-1-11133−3−3−3−333−3−33333−3−300000000000000000000
χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-222-211-1-100000000-1-111−3−33333−3−333−3−3−3−33300000000000000000000
χ372222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-111-1-122-2-2-1-1-1-122-2-222-2-21111-1-1-1-11111-1-1-1-1111100000000000000000000
χ382222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-111-1-122-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-11111-1-1-1-100000000000000000000
χ392222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-111-1-1-2-222111122-2-2-2-222-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ402222-2-2-2-222-2-2-2-2-122-222-2-1-1-11111-1-11111-1-111-1-1-2-2221111-2-22222-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ412222-2-2-2-2-2-222-2-22-222-222222-2-2-2-2-2-222-2-2-2222-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ422222-2-2-2-2-2-222-2-22-222-222222-2-2-2-2-2-222-2-2-2222-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ432222-2-2-2-2-2-2-2-22222-222-22222-2-2-2-2-2-2-2-2222-2222-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ442222-2-2-2-2-2-2-2-22222-222-22222-2-2-2-2-2-2-2-2222-2222-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ452-2-2222-2-22-22-22-2222-2-2-22-2-2222-2-22-22-22-2222-2-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-2-2222-2-22-22-22-2222-2-2-22-2-2222-2-22-22-22-2222-2-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-2-2222-2-22-22-22-2-122-2-2-2211-1-1-111-11-11-11-1-1-11110000−i3i3−i3i300002i−2i2i−2i−i3i3−i3i33−33−33−33−3−ii−ii−ii−ii00000000000000000000
χ482-2-2222-2-22-22-22-2-122-2-2-2211-1-1-111-11-11-11-1-1-11110000−i3i3−i3i30000−2i2i−2i2i−i3i3−i3i3−33−33−33−33i−ii−ii−ii−i00000000000000000000
χ492-2-2222-2-22-22-22-2-122-2-2-2211-1-1-111-11-11-11-1-1-11110000i3−i3i3−i300002i−2i2i−2ii3−i3i3−i3−33−33−33−33−ii−ii−ii−ii00000000000000000000
χ502-2-2222-2-22-22-22-2-122-2-2-2211-1-1-111-11-11-11-1-1-11110000i3−i3i3−i30000−2i2i−2i2ii3−i3i3−i33−33−33−33−3i−ii−ii−ii−i00000000000000000000
χ512-2-2222-2-22-2-22-222-2-2-2222-2-2222-2-22-2-22-22-2-22-222000000002-22-2000000002-2-222-2-220000000000000000000000000000
χ522-2-2222-2-22-2-22-222-2-2-2222-2-2222-2-22-2-22-22-2-22-22200000000-22-2200000000-222-2-222-20000000000000000000000000000
χ532-2-2222-2-22-2-22-22-1-2-2-222211-1-1-111-111-11-111-11-1-10000−i3i3i3−i32-22-20000−i3i3i3−i3-111-1-111-1−i3i3i3−i3−i3i3i3−i300000000000000000000
χ542-2-2222-2-22-2-22-22-1-2-2-222211-1-1-111-111-11-111-11-1-10000−i3i3i3−i3-22-220000−i3i3i3−i31-1-111-1-11i3−i3−i3i3i3−i3−i3i300000000000000000000
χ552-2-2222-2-22-2-22-22-1-2-2-222211-1-1-111-111-11-111-11-1-10000i3−i3−i3i32-22-20000i3−i3−i3i3-111-1-111-1i3−i3−i3i3i3−i3−i3i300000000000000000000
χ562-2-2222-2-22-2-22-22-1-2-2-222211-1-1-111-111-11-111-11-1-10000i3−i3−i3i3-22-220000i3−i3−i3i31-1-111-1-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ572-2-2222-2-2-222-2-2222-22-22-2-2-2222-2-2-222-2-222-2-22-220000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ582-2-2222-2-2-222-2-2222-22-22-2-2-2222-2-2-222-2-222-2-22-22000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ592-2-2222-2-2-22-222-22-2222-2-2-2-2222-2-2-22-222-2-22-222-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ602-2-2222-2-2-22-222-22-2222-2-2-2-2222-2-2-22-222-2-22-222-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ612-2-22-2-2222-22-22-22-2-2222-2-2-22-2-2222-22-22-2-2-2-2222000000002-2-22000000002-2-22-222-20000000000000000000000000000
χ622-2-22-2-2222-22-22-22-2-2222-2-2-22-2-2222-22-22-2-2-2-222200000000-222-200000000-222-22-2-220000000000000000000000000000
χ632-2-22-2-2222-22-22-2-1-2-2222-211-111-1-1-11-11-11111-1-1-10000−i3i3i3−i32-2-220000i3−i3−i3i3-111-11-1-11−i3i3i3−i3i3−i3−i3i300000000000000000000
χ642-2-22-2-2222-22-22-2-1-2-2222-211-111-1-1-11-11-11111-1-1-10000−i3i3i3−i3-222-20000i3−i3−i3i31-1-11-111-1i3−i3−i3i3−i3i3i3−i300000000000000000000
χ652-2-22-2-2222-22-22-2-1-2-2222-211-111-1-1-11-11-11111-1-1-10000i3−i3−i3i32-2-220000−i3i3i3−i3-111-11-1-11i3−i3−i3i3−i3i3i3−i300000000000000000000
χ662-2-22-2-2222-22-22-2-1-2-2222-211-111-1-1-11-11-11111-1-1-10000i3−i3−i3i3-222-20000−i3i3i3−i31-1-11-111-1−i3i3i3−i3i3−i3−i3i300000000000000000000
χ672-2-22-2-2222-2-22-222222-2-2-2-2-22-2-2222-2-22-2222-22-2-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ682-2-22-2-2222-2-22-222222-2-2-2-2-22-2-2222-2-22-2222-22-2-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ692-2-22-2-2222-2-22-22-1222-2-2-211-111-1-1-111-11-1-1-11-1110000−i3i3−i3i300002i−2i−2i2ii3−i3i3−i33−33−3−33−33−ii−iii−ii−i00000000000000000000
χ702-2-22-2-2222-2-22-22-1222-2-2-211-111-1-1-111-11-1-1-11-1110000−i3i3−i3i30000−2i2i2i−2ii3−i3i3−i3−33−333−33−3i−ii−i−ii−ii00000000000000000000
χ712-2-22-2-2222-2-22-22-1222-2-2-211-111-1-1-111-11-1-1-11-1110000i3−i3i3−i300002i−2i−2i2i−i3i3−i3i3−33−333−33−3−ii−iii−ii−i00000000000000000000
χ722-2-22-2-2222-2-22-22-1222-2-2-211-111-1-1-111-11-1-1-11-1110000i3−i3i3−i30000−2i2i2i−2i−i3i3−i3i33−33−3−33−33i−ii−i−ii−ii00000000000000000000
χ732-2-22-2-222-222-2-222-22-22-22-2-22-2-222-222-2-22-222-22-20000000000000000000000000000000000000000000000002-2-220000
χ742-2-22-2-222-222-2-222-22-22-22-2-22-2-222-222-2-22-222-22-2000000000000000000000000000000000000000000000000-222-20000
χ752-2-22-2-222-22-222-222-2-2-222-2-22-2-222-22-222-22-22-2-2200000000000000000000000000000000000022-2-2-2-222000000000000
χ762-2-22-2-222-22-222-222-2-2-222-2-22-2-222-22-222-22-22-2-22000000000000000000000000000000000000-2-22222-2-2000000000000
χ7744444444-4-444-4-4-24-4-44-4-4-2-2-2-2-2-2-222-2-222-2222-2200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-444-2-44-4-44-4-2-2-2-2-2-2-22222-2-22-2222-200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-4-444-4-4-2-444-444-2-2-2222222-2-2222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-4-4-444-24-444-44-2-2-222222222-2-2-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ8144-4-44i−4i4i−4i00000040000004-4-44i−4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ8244-4-44i−4i4i−4i00000040000004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ8344-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ8444-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ854-44-44i−4i−4i4i0000004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000
χ864-44-44i−4i−4i4i0000004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000
χ874-44-4−4i4i4i−4i0000004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000
χ884-44-4−4i4i4i−4i0000004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000
χ894-4-4444-4-4-444-4-44-24-44-44-422-2-2-2222-2-222-2-222-22-200000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-44-444-4-2-4444-4-422-2-2-2222-22-2-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ914-4-44-4-444-444-4-44-2-44-44-4422-222-2-22-2-222-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-444-4-24-4-4-44422-222-2-22-22-2-22-22-222-200000000000000000000000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000000-4000000-444−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8−8i8i−8i8i000000-4000000-4444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88i−8i−8i8i000000-40000004-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i000000-40000004-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.