Finite Group Databasebeta

← Group #10691307

Character table — Group #10691307

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order1222444434444444466612121212222444444412121212121212128888888866688881212121212121224242424242424248888888888884412121212888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-11-1-1-1-1-1-111111111111111111-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-11-1-1-1-1-1-111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-111-1-1-1-111iiii−i−i−i−i-11111-1-11-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−ii−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-111-1-1-1-111iiii−i−i−i−i-111-1-1111-1-111-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i-11-1-111−i−iii−ii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-111-1-1-1-111−i−i−i−iiiii-11111-1-11-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii−ii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-111-1-111-1-1-1-111−i−i−i−iiiii-111-1-1111-1-111-1-1-1-1-1-11111−i−iii−i−i−i−iiiii-11-1-111ii−i−ii−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1111-1-11111-1-1-1-111iiii−i−i−i−i-1-1-111-1-1111-1-1111111-1-1-1-1ii−i−i−i−i−i−iiiii-11-1-111ii−i−i−ii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1111-1-11111-1-1-1-111iiii−i−i−i−i-1-1-1-1-111111-1-111-1-1-1-11111ii−i−i−i−i−i−iiiii1-111-1-1−i−iiii−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1111-1-11111-1-1-1-111−i−i−i−iiiii-1-1-111-1-1111-1-1111111-1-1-1-1−i−iiiiiii−i−i−i−i-11-1-111−i−iiii−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-1-1-1111-1-11111-1-1-1-111−i−i−i−iiiii-1-1-1-1-111111-1-111-1-1-1-11111−i−iiiiiii−i−i−i−i1-111-1-1ii−i−i−ii
χ1722222222222-2-2-2-2222222222-200-20000002222-2-2-2-222222222-2000000-200000000000000-2-2-2-200000000000000000000
χ1822222222222-2-2-2-2222222222-200-20000002222-2-2-2-2-2-2-2-2-2-2-2-2-2000000-200000000000000222200000000000000000000
χ19222222222-2-22222-2-22222222-222-222-2-2-2-2-2-2-2-2222200000000-2220000-222-2-2-2-200000000000000000000000000000000
χ20222222222-2-22222-2-22222222-2-2-2-2-2-22222-2-2-2-2222200000000-2-2-20000-2-2-2222200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222002000000-2-2-2-2-2-2-2-200000000200000020000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-222222222002000000-2-2-2-2-2-2-2-20000000020000002000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-2-2-2-2-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-1112222-1111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-12-2-22-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-111-2-2-2-2-11111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2-22222-2-2-1-1-1-1-1-1-1-222-222-2-2-2-21111-1-1-1-1000000001-1-100001-1-11111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1-2-22222-2-2-1-1-1-1-1-1-1-222-222-2-2-2-21111-1-1-1-1000000001-1-100001-1-11111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000000001110000111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000000001110000111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-2200-200000022-2-222-2-22i2i2i2i−2i−2i−2i−2i2000000-200000000000000−2i−2i2i2i00000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-2200-200000022-2-222-2-2−2i−2i−2i−2i2i2i2i2i2000000-2000000000000002i2i−2i−2i00000000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-2222-2-2-2-2-222-2-222-2-222000000002220000-2-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-22-2-222-2-222222-2-2-2-22-2-2-22222-2-2-2-222-2-222000000002-2-20000-22222-2-200000000000000000000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-2002000000-2-22222-2-200000000-2000000200000000000000000022-2-2-2-222000000000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-2002000000-2-22222-2-200000000-20000002000000000000000000-2-22222-2-2000000000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-2222-2-222-2-2-1-11111-1-1000000001-1-122-2-2-111-1-111-1-1-1-111110000000000002-2-1-111000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-2222-2-222-2-2-1-11111-1-1000000001-1-1-2-222-111-1-1111111-1-1-1-1000000000000-2211-1-1000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-2-2-2222-2-222-1-11111-1-10000000011122-2-2-1-1-111-1-1-1-1-1-11111000000000000-2211-1-1000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-2-2-2222-2-222-1-11111-1-100000000111-2-222-1-1-111-1-11111-1-1-1-10000000000002-2-1-111000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-11111222-2-2-2-2-22211-1-111-1-100000000-1-1-1000011111-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ422222-2-2-2-2-1-2-222-2-222-1-1-11111222-2-2-2-2-22211-1-111-1-100000000-1-1-1000011111-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ432222-2-2-2-2-1-2-222-2-222-1-1-111112-2-2-22222-2-211-1-111-1-100000000-11100001-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-111112-2-2-22222-2-211-1-111-1-100000000-11100001-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ452-22-22i−2i2i−2i2002-22i−2i00-22-22i2i−2i−2i0000002i−2i2-200002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000002i−2i2-2000000001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ462-22-22i−2i2i−2i2002-22i−2i00-22-22i2i−2i−2i0000002i−2i2-200002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000002i−2i2-200000000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ472-22-22i−2i2i−2i2002-22i−2i00-22-22i2i−2i−2i000000−2i2i-2200002i−2i2-21+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−2i2i-22000000001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ482-22-22i−2i2i−2i2002-22i−2i00-22-22i2i−2i−2i000000−2i2i-2200002i−2i2-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−2i2i-2200000000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ492-22-22i−2i2i−2i200-22−2i2i00-22-22i2i−2i−2i02-202i−2i00000000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i02-2000002i−2i000000000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ502-22-22i−2i2i−2i200-22−2i2i00-22-22i2i−2i−2i02-202i−2i00000000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i02-2000002i−2i0000000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ512-22-22i−2i2i−2i200-22−2i2i00-22-22i2i−2i−2i0-220−2i2i00000000−2i2i-221+i1+i−1−i−1−i1−i1−i−1+i−1+i0-2200000−2i2i000000000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ522-22-22i−2i2i−2i200-22−2i2i00-22-22i2i−2i−2i0-220−2i2i00000000−2i2i-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i0-2200000−2i2i0000000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ532-22-2−2i2i−2i2i2002-2−2i2i00-22-2−2i−2i2i2i0000002i−2i-220000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000002i−2i-22000000001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ542-22-2−2i2i−2i2i2002-2−2i2i00-22-2−2i−2i2i2i0000002i−2i-220000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000002i−2i-2200000000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ552-22-2−2i2i−2i2i2002-2−2i2i00-22-2−2i−2i2i2i000000−2i2i2-20000−2i2i2-21−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−2i2i2-2000000001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ562-22-2−2i2i−2i2i2002-2−2i2i00-22-2−2i−2i2i2i000000−2i2i2-20000−2i2i2-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−2i2i2-200000000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ572-22-2−2i2i−2i2i200-222i−2i00-22-2−2i−2i2i2i02-20−2i2i000000002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i02-200000−2i2i000000000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ582-22-2−2i2i−2i2i200-222i−2i00-22-2−2i−2i2i2i02-20−2i2i000000002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i02-200000−2i2i0000000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ592-22-2−2i2i−2i2i200-222i−2i00-22-2−2i−2i2i2i0-2202i−2i000000002i−2i-221−i1−i−1+i−1+i1+i1+i−1−i−1−i0-22000002i−2i000000000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ602-22-2−2i2i−2i2i200-222i−2i00-22-2−2i−2i2i2i0-2202i−2i000000002i−2i-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i0-22000002i−2i0000000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ612-2-222i−2i−2i2i22-200002i−2i-2-222i−2i2i−2i00000000002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130002−2−i2i200000002−22−2−i2i2−i2i20000000000000000001+i−1−i1−i−1+i00
χ622-2-222i−2i−2i2i22-200002i−2i-2-222i−2i2i−2i00000000002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000−22i2−i20000000−22−22i2−i2i2−i2000000000000000000−1−i1+i−1+i1−i00
χ632-2-222i−2i−2i2i22-200002i−2i-2-222i−2i2i−2i00000000002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130002−2−i2i200000002−22−2−i2i2−i2i2000000000000000000−1−i1+i−1+i1−i00
χ642-2-222i−2i−2i2i22-200002i−2i-2-222i−2i2i−2i00000000002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000−22i2−i20000000−22−22i2−i2i2−i20000000000000000001+i−1−i1−i−1+i00
χ652-2-22−2i2i2i−2i22-20000−2i2i-2-22−2i2i−2i2i00000000002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230002−2i2−i200000002−22−2i2−i2i2−i20000000000000000001−i−1+i1+i−1−i00
χ662-2-22−2i2i2i−2i22-20000−2i2i-2-22−2i2i−2i2i00000000002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000−22−i2i20000000−22−22−i2i2−i2i2000000000000000000−1+i1−i−1−i1+i00
χ672-2-22−2i2i2i−2i22-20000−2i2i-2-22−2i2i−2i2i00000000002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230002−2i2−i200000002−22−2i2−i2i2−i2000000000000000000−1+i1−i−1−i1+i00
χ682-2-22−2i2i2i−2i22-20000−2i2i-2-22−2i2i−2i2i00000000002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000−22−i2i20000000−22−22−i2i2−i2i20000000000000000001−i−1+i1+i−1−i00
χ6944444444-244-4-4-4-444-2-2-2-2-2-2-2-400-4000000-2-2-2-22222000000002000000200000000000000000000000000000000000000
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χ814-44-4−4i4i−4i4i-2004-4−4i4i002-222i2i−2i−2i0000004i−4i-4400002i−2i-22000000000000000000−2i2i2-200000000000000000000000000000000
χ824-44-4−4i4i−4i4i-2004-4−4i4i002-222i2i−2i−2i000000−4i4i4-400002i−2i-220000000000000000002i−2i-2200000000000000000000000000000000
χ834-44-4−4i4i−4i4i-200-444i−4i002-222i2i−2i−2i04-40−4i4i00000000−2i2i2-2000000000-22000002i−2i000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i-200-444i−4i002-222i2i−2i−2i0-4404i−4i00000000−2i2i2-20000000002-200000−2i2i000000000000000000000000000000000000
χ854-4-444i−4i−4i4i4-440000−4i4i-4-444i−4i4i−4i0000000000-44−4i4i0000000000000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i-24-400004i−4i22-2−2i2i−2i2i0000000000-22−2i2i00000000000000022−22−2i22i20000000−22−22i2−i2i2−i2000000000000000000000000
χ874-4-444i−4i−4i4i-24-400004i−4i22-2−2i2i−2i2i0000000000-22−2i2i000000000000000−22222i2−2i200000002−22−2−i2i2−i2i2000000000000000000000000
χ884-4-444i−4i−4i4i-2-440000−4i4i22-2−2i2i−2i2i00000000002-22i−2i00000000000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ894-4-444i−4i−4i4i-2-440000−4i4i22-2−2i2i−2i2i00000000002-22i−2i00000000000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ904-4-44−4i4i4i−4i4-4400004i−4i-4-44−4i4i−4i4i0000000000-444i−4i0000000000000000000000000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i-24-40000−4i4i22-22i−2i2i−2i0000000000-222i−2i00000000000000022−222i2−2i20000000−22−22−i2i2−i2i2000000000000000000000000
χ924-4-44−4i4i4i−4i-24-40000−4i4i22-22i−2i2i−2i0000000000-222i−2i000000000000000−2222−2i22i200000002−22−2i2−i2i2−i2000000000000000000000000
χ934-4-44−4i4i4i−4i-2-4400004i−4i22-22i−2i2i−2i00000000002-2−2i2i00000000000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ944-4-44−4i4i4i−4i-2-4400004i−4i22-22i−2i2i−2i00000000002-2−2i2i00000000000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ9588-8-888-8-8-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-8-888-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000000000000000

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