Finite Group Databasebeta

← Group #10705297

Character table — Group #10705297

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122244443444466688888888121212122444668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616888824242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11
χ121111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-1
χ131111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ141111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ151111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222-2-2-2-222200000000222222-2-2220000-2-2-2-222-2-2-2-2000000000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222-2-2-2-222200000000222222-2-2220000-2-2-2-222-2-2-2-20000000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222-2-2-2-2222000000002222-2-222-2-20000-2-222-2-222-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222-2-2-2-2222000000002222-2-222-2-20000-2-222-2-222-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-12222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-12222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-12222-1-1-122222222-1-1-1-1-2-2-2-211-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-12222-1-1-122222222-1-1-1-1-2-2-2-211-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ2722222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2112222-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-2112222-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-222200000000-2-2-2-22-2-2222000022-2-2-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ322222-2-2-2-2222-2-222200000000-2-2-2-22-2-2222000022-2-2-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ332222-2-2-2-2222-2-222200000000-2-2-2-2-222-2-2-20000222222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2222-2-222200000000-2-2-2-2-222-2-2-20000222222-2-2-2-20000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-22-22-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ362222-2-2-2-22-2-222222-2-2-2-22222-2-2-2-2-22-22-2-222-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ372222-2-2-2-2-1-2-222-1-1-12222-2-2-2-211112-22-2-1-122-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ382222-2-2-2-2-1-2-222-1-1-12222-2-2-2-211112-22-2-1-122-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ392222-2-2-2-2-1-2-222-1-1-12222-2-2-2-21111-22-2211-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ402222-2-2-2-2-1-2-222-1-1-12222-2-2-2-21111-22-2211-2-2221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ412222-2-2-2-2-1-2-222-1-1-1-2-2-2-2222211112-22-2-1-1-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-1000000000000000000003−3−333−3−330000
χ422222-2-2-2-2-1-2-222-1-1-1-2-2-2-2222211112-22-2-1-1-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−333−3−333−30000
χ432222-2-2-2-2-1-2-222-1-1-1-2-2-2-222221111-22-221122-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ442222-2-2-2-2-1-2-222-1-1-1-2-2-2-222221111-22-221122-2-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ452-22-22i2i−2i−2i22i−2i2-22-2-2000000002i2i−2i−2i0000002i−2i2-22i−2i0000002-2000000002i2i−2i−2i22-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ462-22-22i2i−2i−2i22i−2i2-22-2-2000000002i2i−2i−2i0000002i−2i2-22i−2i0000002-2000000002i2i−2i−2i22-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ472-22-22i2i−2i−2i22i−2i2-22-2-2000000002i2i−2i−2i000000−2i2i-222i−2i0000002-200000000−2i−2i2i2i-2-2221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ482-22-22i2i−2i−2i22i−2i2-22-2-2000000002i2i−2i−2i000000−2i2i-222i−2i0000002-200000000−2i−2i2i2i-2-222−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ492-22-22i2i−2i−2i2−2i2i-222-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i000000-2222-2-22i2i−2i−2i0000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ502-22-22i2i−2i−2i2−2i2i-222-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000−2i2i000000-2222-2-22i2i−2i−2i00000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ512-22-22i2i−2i−2i2−2i2i-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000−2i2i000000-22-2-222−2i−2i2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ522-22-22i2i−2i−2i2−2i2i-222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000−2i2i000000-22-2-222−2i−2i2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ532-22-2−2i−2i2i2i22i−2i-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i000000-2222-2-2−2i−2i2i2i00000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ542-22-2−2i−2i2i2i22i−2i-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000002i−2i000000-2222-2-2−2i−2i2i2i0000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ552-22-2−2i−2i2i2i22i−2i-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000002i−2i000000-22-2-2222i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ562-22-2−2i−2i2i2i22i−2i-222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000002i−2i000000-22-2-2222i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ572-22-2−2i−2i2i2i2−2i2i2-22-2-200000000−2i−2i2i2i0000002i−2i-22−2i2i0000002-2000000002i2i−2i−2i-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ582-22-2−2i−2i2i2i2−2i2i2-22-2-200000000−2i−2i2i2i0000002i−2i-22−2i2i0000002-2000000002i2i−2i−2i-2-222−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ592-22-2−2i−2i2i2i2−2i2i2-22-2-200000000−2i−2i2i2i000000−2i2i2-2−2i2i0000002-200000000−2i−2i2i2i22-2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ602-22-2−2i−2i2i2i2−2i2i2-22-2-200000000−2i−2i2i2i000000−2i2i2-2−2i2i0000002-200000000−2i−2i2i2i22-2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ6144444444-2-4-4-4-4-2-2-200000000-2-2-2-244-4-4-2-200002222-2-22222000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-200000000-2-2-2-2-4-44422000022-2-222-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-2-2-20000000022224-4-44-2-20000-2-22222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-244-4-4-2-2-2000000002222-444-4220000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-44-440000-44-422−2222−2222−2222−224-44-40000000000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ6644-4-44-44-440000-44-4−2222−2222−2222−22224-44-400000000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
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χ6944-4-44-44-4-200002-22−2222−2222−2222−2222-22-2200000000000023−230023−23002−22−22−22−2−66−66−66−6600000000000000000000000000000000
χ7044-4-44-44-4-200002-22−2222−2222−2222−2222-22-22000000000000−232300−2323002−22−22−22−26−66−66−66−600000000000000000000000000000000
χ7144-4-4-44-4440000-44-422−2222−22−2222−2222-44-440000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000
χ7244-4-4-44-4440000-44-4−2222−222222−2222−22-44-4400000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000
χ7344-4-4-44-44-200002-2222−2222−22−2222−22222-22-200000000000023−2300−232300−22−222−22−26−66−6−66−6600000000000000000000000000000000
χ7444-4-4-44-44-200002-2222−2222−22−2222−22222-22-2000000000000−23230023−2300−22−222−22−2−66−666−66−600000000000000000000000000000000
χ7544-4-4-44-44-200002-22−2222−222222−2222−222-22-200000000000023−2300−2323002−22−2−22−22−66−666−66−600000000000000000000000000000000
χ7644-4-4-44-44-200002-22−2222−222222−2222−222-22-2000000000000−23230023−23002−22−2−22−226−66−6−66−6600000000000000000000000000000000
χ774-44-44i4i−4i−4i-24i−4i4-4-22200000000−2i−2i2i2i0000004i−4i4-4−2i2i000000-2200000000−2i−2i2i2i-2-22200000000000000000000000000000000
χ784-44-44i4i−4i−4i-24i−4i4-4-22200000000−2i−2i2i2i000000−4i4i-44−2i2i000000-22000000002i2i−2i−2i22-2-200000000000000000000000000000000
χ794-44-44i4i−4i−4i-2−4i4i-44-22244-4-44i4i−4i−4i−2i−2i2i2i00000000002i−2i0000002-2-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ804-44-44i4i−4i−4i-2−4i4i-44-222-4-444−4i−4i4i4i−2i−2i2i2i00000000002i−2i0000002-222-2-22i2i−2i−2i0000000000000000000000000000000000000000
χ814-44-4−4i−4i4i4i-24i−4i-44-22244-4-4−4i−4i4i4i2i2i−2i−2i0000000000−2i2i0000002-2-2-2222i2i−2i−2i0000000000000000000000000000000000000000
χ824-44-4−4i−4i4i4i-24i−4i-44-222-4-4444i4i−4i−4i2i2i−2i−2i0000000000−2i2i0000002-222-2-2−2i−2i2i2i0000000000000000000000000000000000000000
χ834-44-4−4i−4i4i4i-2−4i4i4-4-222000000002i2i−2i−2i0000004i−4i-442i−2i000000-2200000000−2i−2i2i2i22-2-200000000000000000000000000000000
χ844-44-4−4i−4i4i4i-2−4i4i4-4-222000000002i2i−2i−2i000000−4i4i4-42i−2i000000-22000000002i2i−2i−2i-2-22200000000000000000000000000000000
χ854-4-444i−4i−4i4i40000-4-4422−22−22222i2−2i2−2i22i24i−4i−4i4i0000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i40000-4-44−222222−22−2i22i22i2−2i24i−4i−4i4i00000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i-2000022-222−22−22222i2−2i2−2i22i2−2i2i2i−2i0000−2i32i30000000023−230000−222−2−i2i2i2−i2i6−i6−i6i66−6−6600000000000000000000000000000000
χ884-4-444i−4i−4i4i-2000022-222−22−22222i2−2i2−2i22i2−2i2i2i−2i00002i3−2i300000000−23230000−222−2−i2i2i2−i2−i6i6i6−i6−666−600000000000000000000000000000000
χ894-4-444i−4i−4i4i-2000022-2−222222−22−2i22i22i2−2i2−2i2i2i−2i0000−2i32i30000000023−2300002−2−22i2−i2−i2i2−i6i6i6−i6−666−600000000000000000000000000000000
χ904-4-444i−4i−4i4i-2000022-2−222222−22−2i22i22i2−2i2−2i2i2i−2i00002i3−2i300000000−232300002−2−22i2−i2−i2i2i6−i6−i6i66−6−6600000000000000000000000000000000
χ914-4-44−4i4i4i−4i40000-4-4422−22−2222−2i22i22i2−2i2−4i4i4i−4i0000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i40000-4-44−222222−222i2−2i2−2i22i2−4i4i4i−4i00000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i-2000022-222−22−2222−2i22i22i2−2i22i−2i−2i2i0000−2i32i300000000−23230000−222−2i2−i2−i2i2i6−i6−i6i6−666−600000000000000000000000000000000
χ944-4-44−4i4i4i−4i-2000022-222−22−2222−2i22i22i2−2i22i−2i−2i2i00002i3−2i30000000023−230000−222−2i2−i2−i2i2−i6i6i6−i66−6−6600000000000000000000000000000000
χ954-4-44−4i4i4i−4i-2000022-2−222222−222i2−2i2−2i22i22i−2i−2i2i0000−2i32i300000000−232300002−2−22−i2i2i2−i2−i6i6i6−i66−6−6600000000000000000000000000000000
χ964-4-44−4i4i4i−4i-2000022-2−222222−222i2−2i2−2i22i22i−2i−2i2i00002i3−2i30000000023−2300002−2−22−i2i2i2−i2i6−i6−i6i6−666−600000000000000000000000000000000

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