Finite Group Databasebeta

← Group #10691448

Character table — Group #10691448

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444121212121212121212121212121212121616161616161616161616162424242424242424
order12224444223444444444444446661212121244444466121212121212121212121212121212121212121212121212121244444444444444444488121212122424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1-1-1111iiii−i−i−i−i11-1-1111-1-1-1-11-1ii−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1-1-1-1-1111iiii−i−i−i−i11-1-1111-1-1-1-11-1ii−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−i−iii
χ111111-1-1-1-1-1-1111iiii−i−i−i−i11-1-1111-1-1-1-11-1ii−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-1-111−i−iii
χ121111-1-1-1-1-1-1111iiii−i−i−i−i11-1-1111-1-1-1-11-1ii−i−i-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii11-1-1ii−i−i
χ131111-1-1-1-1-1-1111−i−i−i−iiiii11-1-1111-1-1-1-11-1−i−iii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−i−iii
χ141111-1-1-1-1-1-1111−i−i−i−iiiii11-1-1111-1-1-1-11-1−i−iii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111ii−i−i
χ151111-1-1-1-1-1-1111−i−i−i−iiiii11-1-1111-1-1-1-11-1−i−iii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-1-111ii−i−i
χ161111-1-1-1-1-1-1111−i−i−i−iiiii11-1-1111-1-1-1-11-1−i−iii-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222222-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ192222222222-122222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000
χ202222222222-122222222222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-21111111100000000
χ212222222222-12222222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ222222222222-12222222222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-111111111-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ232222222222-122-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-1111100000000
χ242222222222-122-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-100000000
χ252222222222-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ262222222222-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-1-1-1-1111111111111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ2722222222-2-22-2-20000000022222222222-2-20000-2-2-2-222-2-222-2-2000000000000000022-2-222-2-20000000000000000000000000000
χ2822222222-2-22-2-20000000022222222222-2-20000-2-2-2-222-2-222-2-20000000000000000-2-222-2-2220000000000000000000000000000
χ2922222222-2-22-2-200000000-2-2-2-22222222220000-2-2-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3022222222-2-22-2-200000000-2-2-2-22222222220000-2-2-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ312222-2-2-2-2222-2-20000000022-2-2222-2-2-2-2-22000022-2-222-2-2-2-222000000000000000022-2-2-2-2220000000000000000000000000000
χ322222-2-2-2-2222-2-20000000022-2-2222-2-2-2-2-22000022-2-222-2-2-2-2220000000000000000-2-22222-2-20000000000000000000000000000
χ332222-2-2-2-2222-2-200000000-2-222222-2-2-2-22-2000022-2-2-2-22222-2-200000000000000000000000022-2-2-2-22200000000000000000000
χ342222-2-2-2-2222-2-200000000-2-222222-2-2-2-22-2000022-2-2-2-22222-2-2000000000000000000000000-2-22222-2-200000000000000000000
χ352222-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-222222-2-2-2-2-22−2i−2i2i2i-2-222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-222222-2-2-2-2-222i2i−2i−2i-2-222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i22-2-2-1-1-111112-22i2i−2i−2i11-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii00000000
χ382222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i22-2-2-1-1-111112-22i2i−2i−2i11-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i00000000
χ392222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i-2-222-1-1-11111-22−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−3300000000
χ402222-2-2-2-2-2-2-1222i2i2i2i−2i−2i−2i−2i-2-222-1-1-11111-22−2i−2i2i2i11-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ412222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i22-2-2-1-1-111112-2−2i−2i2i2i11-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i00000000
χ422222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i22-2-2-1-1-111112-2−2i−2i2i2i11-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii00000000
χ432222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i-2-222-1-1-11111-222i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−300000000
χ442222-2-2-2-2-2-2-122−2i−2i−2i−2i2i2i2i2i-2-222-1-1-11111-222i2i−2i−2i11-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−3300000000
χ4522-2-222-2-22-222-222-2-222-2-200002-2-222-2-20000002-22-20000000022-2-2000022-2-2000000000000000000000000000000002−22−22−22−2
χ4622-2-222-2-22-222-222-2-222-2-200002-2-222-2-20000002-22-20000000022-2-2000022-2-200000000000000000000000000000000−22−22−22−22
χ4722-2-222-2-22-222-2-2-222-2-22200002-2-222-2-20000002-22-200000000-2-2220000-2-222000000000000000000000000000000002−22−2−22−22
χ4822-2-222-2-22-222-2-2-222-2-22200002-2-222-2-20000002-22-200000000-2-2220000-2-22200000000000000000000000000000000−22−222−22−2
χ4922-2-2-2-222-2222-22i2i−2i−2i−2i−2i2i2i00002-2-2-2-222000000-222-2000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000000000002−2−22i2−i2−i2i2
χ5022-2-2-2-222-2222-22i2i−2i−2i−2i−2i2i2i00002-2-2-2-222000000-222-2000000002i2i−2i−2i0000−2i−2i2i2i00000000000000000000000000000000−222−2−i2i2i2−i2
χ5122-2-2-2-222-2222-2−2i−2i2i2i2i2i−2i−2i00002-2-2-2-222000000-222-200000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000000000002−2−22−i2i2i2−i2
χ5222-2-2-2-222-2222-2−2i−2i2i2i2i2i−2i−2i00002-2-2-2-222000000-222-200000000−2i−2i2i2i00002i2i−2i−2i00000000000000000000000000000000−222−2i2−i2−i2i2
χ532-22-22i−2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i-22-22i−2i2i−2i001+i−1−i1−i−1+i00002-2002i−2i001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i002i−2i002-21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ542-22-22i−2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i-22-22i−2i2i−2i001+i−1−i1−i−1+i00002-2002i−2i001+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i00−2i2i00-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ552-22-22i−2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i-22-22i−2i2i−2i00−1−i1+i−1+i1−i0000-2200−2i2i001+i−1−i1+i−1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i−1+i−1+i1−i1−i2-2002i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000
χ562-22-22i−2i2i−2i002001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i-22-22i−2i2i−2i00−1−i1+i−1+i1−i0000-2200−2i2i001+i−1−i1+i−1−i−1−i−1−i1+i1+i1−i−1+i1−i−1+i−1+i−1+i1−i1−i-2200−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000
χ572-22-22i−2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i-22-22i−2i2i−2i00−1−i1+i−1+i1−i00002-2002i−2i00−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i002i−2i002-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ582-22-22i−2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i-22-22i−2i2i−2i00−1−i1+i−1+i1−i00002-2002i−2i00−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i00−2i2i00-221−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ592-22-22i−2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i-22-22i−2i2i−2i001+i−1−i1−i−1+i0000-2200−2i2i00−1−i1+i−1−i1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i1−i1−i−1+i−1+i2-2002i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000000000
χ602-22-22i−2i2i−2i00200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i-22-22i−2i2i−2i001+i−1−i1−i−1+i0000-2200−2i2i00−1−i1+i−1−i1+i1+i1+i−1−i−1−i−1+i1−i−1+i1−i1−i1−i−1+i−1+i-2200−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000000000
χ612-22-2−2i2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i-22-2−2i2i−2i2i001−i−1+i1+i−1−i00002-200−2i2i001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i002i−2i00-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ622-22-2−2i2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i-22-2−2i2i−2i2i001−i−1+i1+i−1−i00002-200−2i2i001−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i00−2i2i002-21+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ632-22-2−2i2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i-22-2−2i2i−2i2i00−1+i1−i−1−i1+i0000-22002i−2i001−i−1+i1−i−1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i−1−i−1−i1+i1+i2-200−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000
χ642-22-2−2i2i−2i2i002001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i-22-2−2i2i−2i2i00−1+i1−i−1−i1+i0000-22002i−2i001−i−1+i1−i−1+i−1+i−1+i1−i1−i1+i−1−i1+i−1−i−1−i−1−i1+i1+i-22002i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000
χ652-22-2−2i2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i-22-2−2i2i−2i2i00−1+i1−i−1−i1+i00002-200−2i2i00−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i002i−2i00-221+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ662-22-2−2i2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i-22-2−2i2i−2i2i00−1+i1−i−1−i1+i00002-200−2i2i00−1+i1−i−1+i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1−i−1−i1+i1+i00−2i2i002-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ672-22-2−2i2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i-22-2−2i2i−2i2i001−i−1+i1+i−1−i0000-22002i−2i00−1+i1−i−1+i1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i1+i1+i−1−i−1−i2-200−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000000000
χ682-22-2−2i2i−2i2i00200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i-22-2−2i2i−2i2i001−i−1+i1+i−1−i0000-22002i−2i00−1+i1−i−1+i1−i1−i1−i−1+i−1+i−1−i1+i−1−i1+i1+i1+i−1−i−1−i-22002i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.