Finite Group Databasebeta

← Group #10693883

Character table — Group #10693883

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12224444223444444666121212124466888888881212121212128888888888881212242424242424242424242424242424248888888888888824242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-111111-1-1-1-111-1-11-1ii−i−iii−i−i1111-1-1-1-111-1-1iiii−i−i−i−ii−iii−i−i11-1-1i−i
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-111111-1-1-1-1-1-1111-1ii−i−iii−i−i-1-1-1-1111111-1-1iiii−i−i−i−i−ii−i−iii-1-111−ii
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11-1-1-1-1111111-1-11-1ii−i−iii−i−i1111-1-1-1-1-1-111−i−i−i−iiiiii−iii−i−i-1-111−ii
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−iii−i−i111-1-11-1-1-1-11111-1-1111-1ii−i−iii−i−i-1-1-1-11111-1-111−i−i−i−iiiii−ii−i−iii11-1-1i−i
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii111-1-111111-1-1-1-111-1-11-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−iiiii−ii−i−iii11-1-1−ii
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii111-1-111111-1-1-1-1-1-1111-1−i−iii−i−iii-1-1-1-1111111-1-1−i−i−i−iiiiii−iii−i−i-1-111i−i
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11-1-1-1-1111111-1-11-1−i−iii−i−iii1111-1-1-1-1-1-111iiii−i−i−i−i−ii−i−iii-1-111i−i
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii−i−iii111-1-11-1-1-1-11111-1-1111-1−i−iii−i−iii-1-1-1-11111-1-111iiii−i−i−i−ii−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-222222222-2-2222222-2-2-2-22-2-2-2-22000000000000-2-2-2-2-2-2222200000000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-222-2-2-2-222222-2-2-2-22000000000000-2-22222-2-2-2-200000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ232222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-2-11111-1000000000000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ242222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-12222-2-2-2-2-11111-1000000000000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ252222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-2-2-2-22222-11111-100000000000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ262222222222-12-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-2-2-2-22222-11111-100000000000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ2722222222-2-22-22222-22222222-2-2-2-200000000-22222-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ2822222222-2-22-22222-22222222-2-2-2-200000000-22222-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ2922222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ3022222222-2-22-2-2-2-2-2-2222222222-2-200000000-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-222200000000-222-2-2-22222-2-2-2-20000-220000000000000000-2-22200000000000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-222200000000-222-2-2-2-2-2-2-222220000-22000000000000000022-2-200000000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-2-222-20000000000002-20000000000000000000022-2-2-2-222000000000000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-22200000000-2-2-222-20000000000002-200000000000000000000-2-22222-2-2000000000000
χ352222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22i2i−2i−2i−2i−2i2i2i2-2-2222000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ362222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-2−2i−2i2i2i2i2i−2i−2i2-2-2222000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ372222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-1-111-10000000022-2-2-11−i−iii−i−iii-1-1-1-111110000000000002i−2i−i−iii000000
χ382222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i2i2i−2i−2i-1-1-111-100000000-2-222-11−i−iii−i−iii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ392222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-1-111-10000000022-2-2-11ii−i−iii−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ402222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i−2i−2i2i2i-1-1-111-100000000-2-222-11ii−i−iii−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ412222-2-2-2-2-2-2-12-2-2222-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-111-1-1-10000000000001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3000000000000003−3−33000000
χ422222-2-2-2-2-2-2-12-2-2222-1-1-11111-22112i2i−2i−2i−2i−2i2i2i-111-1-1-10000000000001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000000000−333−3000000
χ432222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-111-1-1-10000000000001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000000000−333−3000000
χ442222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211−2i−2i2i2i2i2i−2i−2i-111-1-1-10000000000001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3000000000000003−3−33000000
χ4522-2-222-2-22-2220000-22-2-2-2-222002-22-22-20000-200002−i2−i2i2i2−i2−i2i2i200000000002-22-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4622-2-222-2-22-2220000-22-2-2-2-222002-22-22-20000-200002i2i2−i2−i2i2i2−i2−i200000000002-22-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4722-2-222-2-22-2220000-22-2-2-2-222002-2-22-220000-200002−i2−i2i2i2−i2−i2i2i20000000000-22-2200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4822-2-222-2-22-2220000-22-2-2-2-222002-2-22-220000-200002i2i2−i2−i2i2i2−i2−i20000000000-22-2200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4922-2-222-2-2-222-2000022-2-2-2-22200-2200002i−2i2i−2i20000-2−i2−i2i2i2−i2−i2i2i20000002i−2i2i−2i000000000000i2−i2i2−i22−2−222−2−22000000000000
χ5022-2-222-2-2-222-2000022-2-2-2-22200-2200002i−2i2i−2i20000-2i2i2−i2−i2i2i2−i2−i20000002i−2i2i−2i000000000000−i2i2−i2i2−222−2−222−2000000000000
χ5122-2-222-2-2-222-2000022-2-2-2-22200-220000−2i2i−2i2i20000-2−i2−i2i2i2−i2−i2i2i2000000−2i2i−2i2i000000000000i2−i2i2−i2−222−2−222−2000000000000
χ5222-2-222-2-2-222-2000022-2-2-2-22200-220000−2i2i−2i2i20000-2i2i2−i2−i2i2i2−i2−i2000000−2i2i−2i2i000000000000−i2i2−i2i22−2−222−2−22000000000000
χ5322-2-2-2-2222-22-2000022-2-222-2-2002-200002-2-2220000-2−i2−i2i2i2i2i2−i2−i20000002-2-22000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ5422-2-2-2-2222-22-2000022-2-222-2-2002-200002-2-2220000-2i2i2−i2−i2−i2−i2i2i20000002-2-22000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ5522-2-2-2-2222-22-2000022-2-222-2-2002-20000-222-220000-2−i2−i2i2i2i2i2−i2−i2000000-222-2000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ5622-2-2-2-2222-22-2000022-2-222-2-2002-20000-222-220000-2i2i2−i2−i2−i2−i2i2i2000000-222-2000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ5722-2-2-2-222-22220000-22-2-222-2-200-222i−2i−2i2i0000-200002−i2−i2i2i2i2i2−i2−i200000000002i−2i−2i2i00000000−i2i2i2−i22−22−2−22−22000000000000
χ5822-2-2-2-222-22220000-22-2-222-2-200-222i−2i−2i2i0000-200002i2i2−i2−i2−i2−i2i2i200000000002i−2i−2i2i00000000i2−i2−i2i2−22−222−22−2000000000000
χ5922-2-2-2-222-22220000-22-2-222-2-200-22−2i2i2i−2i0000-200002−i2−i2i2i2i2i2−i2−i20000000000−2i2i2i−2i00000000−i2i2i2−i2−22−222−22−2000000000000
χ6022-2-2-2-222-22220000-22-2-222-2-200-22−2i2i2i−2i0000-200002i2i2−i2−i2−i2−i2i2i20000000000−2i2i2i−2i00000000i2−i2−i2i22−22−2−22−22000000000000
χ612-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i00000000000002-22i−2i02-22-22i−2i2i−2i2−2−i2i200000000002−22−2−i2i2−i2i20000000000000000002−2−i2i200
χ622-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i00000000000002-22i−2i02-22-22i−2i2i−2i−22i2−i20000000000−22−22i2−i2i2−i2000000000000000000−22i2−i200
χ632-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i00000000000002-22i−2i0-22-22−2i2i−2i2i2−2−i2i200000000002−22−2−i2i2−i2i2000000000000000000−22i2−i200
χ642-22-22i−2i2i−2i00202-22i−2i0-22-22i−2i2i−2i00000000000002-22i−2i0-22-22−2i2i−2i2i−22i2−i20000000000−22−22i2−i2i2−i20000000000000000002−2−i2i200
χ652-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i00000000000002-2−2i2i02-22-2−2i2i−2i2i2−2i2−i200000000002−22−2i2−i2i2−i20000000000000000002−2i2−i200
χ662-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i00000000000002-2−2i2i02-22-2−2i2i−2i2i−22−i2i20000000000−22−22−i2i2−i2i2000000000000000000−22−i2i200
χ672-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i00000000000002-2−2i2i0-22-222i−2i2i−2i2−2i2−i200000000002−22−2i2−i2i2−i2000000000000000000−22−i2i200
χ682-22-2−2i2i−2i2i00202-2−2i2i0-22-2−2i2i−2i2i00000000000002-2−2i2i0-22-222i−2i2i−2i−22−i2i20000000000−22−22−i2i2−i2i20000000000000000002−2i2−i200
χ6944444444-4-4-2-44444-4-2-2-2-2-2-2-2-4-422000000002-2-2-2-22000000000000220000000000000000000000000000000000000000
χ7044444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-2442200000000222222000000000000-2-20000000000000000000000000000000000000000
χ714444-4-4-4-444-2-444-4-4-4-2-2-22222-44-2-2000000002-2-22220000000000002-20000000000000000000000000000000000000000
χ724444-4-4-4-444-2-4-4-444-4-2-2-222224-4-2-200000000222-2-22000000000000-220000000000000000000000000000000000000000
χ7344-4-444-4-44-4-240000-4-22222-2-200-224-44-4000020000-2000000000000000000-22-2200000000000000000000000000000000
χ7444-4-444-4-44-4-240000-4-22222-2-200-22-44-44000020000-20000000000000000002-22-200000000000000000000000000000000
χ7544-4-444-4-4-44-2-400004-22222-2-2002-200004i−4i4i−4i-20000200000000000000−2i2i−2i2i000000000000000000000000000000000000
χ7644-4-444-4-4-44-2-400004-22222-2-2002-20000−4i4i−4i4i-200002000000000000002i−2i2i−2i000000000000000000000000000000000000
χ7744-4-4-4-4444-4-2-400004-222-2-22200-2200004-4-44-20000200000000000000-222-2000000000000000000000000000000000000
χ7844-4-4-4-4444-4-2-400004-222-2-22200-220000-444-4-200002000000000000002-2-22000000000000000000000000000000000000
χ7944-4-4-4-444-44-240000-4-222-2-222002-24i−4i−4i4i000020000-2000000000000000000−2i2i2i−2i00000000000000000000000000000000
χ8044-4-4-4-444-44-240000-4-222-2-222002-2−4i4i4i−4i000020000-20000000000000000002i−2i−2i2i00000000000000000000000000000000
χ814-44-44i−4i4i−4i0040-44−4i4i0-44-44i−4i4i−4i0000000000000-44−4i4i0000000000000000000000000000000000000000000000000000000
χ824-44-44i−4i4i−4i00-204-44i−4i02-22−2i2i−2i2i0000000000000-22−2i2i00000000022−22−2i22i20000000000−22−22i2−i2i2−i2000000000000000000000000
χ834-44-44i−4i4i−4i00-204-44i−4i02-22−2i2i−2i2i0000000000000-22−2i2i000000000−22222i2−2i200000000002−22−2−i2i2−i2i2000000000000000000000000
χ844-44-44i−4i4i−4i00-20-44−4i4i02-22−2i2i−2i2i00000000000002-22i−2i00000000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ854-44-44i−4i4i−4i00-20-44−4i4i02-22−2i2i−2i2i00000000000002-22i−2i00000000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ864-44-4−4i4i−4i4i0040-444i−4i0-44-4−4i4i−4i4i0000000000000-444i−4i0000000000000000000000000000000000000000000000000000000
χ874-44-4−4i4i−4i4i00-204-4−4i4i02-222i−2i2i−2i0000000000000-222i−2i00000000022−222i2−2i20000000000−22−22−i2i2−i2i2000000000000000000000000
χ884-44-4−4i4i−4i4i00-204-4−4i4i02-222i−2i2i−2i0000000000000-222i−2i000000000−2222−2i22i200000000002−22−2i2−i2i2−i2000000000000000000000000
χ894-44-4−4i4i−4i4i00-20-444i−4i02-222i−2i2i−2i00000000000002-2−2i2i00000000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ904-44-4−4i4i−4i4i00-20-444i−4i02-222i−2i2i−2i00000000000002-2−2i2i00000000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ914-4-444i−4i−4i4i004000000-4-44−4i4i4i−4i000000000000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000000000000000
χ924-4-444i−4i−4i4i004000000-4-44−4i4i4i−4i0000000000000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i004000000-4-444i−4i−4i4i000000000000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000000000000000
χ944-4-44−4i4i4i−4i004000000-4-444i−4i−4i4i0000000000000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000000000000000
χ958-8-888i−8i−8i8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000

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