Finite Group Databasebeta

← Group #10690166

Character table — Group #10690166

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order12224444223446661212121222224444666666121212121212446688888888121212121212242424242424242424242424242424244444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11-1-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11-1-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11-1-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ131111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1ii−i−i−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1−i−iiiii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222222222-2-2-2-222222222222222-2-2-2-200000000-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222-2-2000000002222-2-200000000000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ222222222222-122-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ232222222222-122-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-11111-2-2-1-12222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ242222222222-122-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-11111-2-2-1-1-2-2-2-222221111-1-111111111-1-1-1-1-1-1-1-10000000000000000
χ252222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111221100000000-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111221100000000-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-22-2-22222222002-22-200-2-20000-2-20000002-200002-22-200002-2000000002-22-22-22-20000000000000000
χ2822222222-2-22-2-22222222002-22-200-2-20000-2-20000002-20000-22-2200002-200000000-22-22-22-220000000000000000
χ2922222222-2-22-2-2222222200-22-2200-2-20000-2-2000000-222-22-200000000-222-22-22-22-2000000000000000000000000
χ3022222222-2-22-2-2222222200-22-2200-2-20000-2-2000000-22-22-2200000000-22-22-22-22-22000000000000000000000000
χ3122222222-2-2-1-2-2-1-1-1-1-1-1-1002-22-20011−i3−i3i3i311−i3−i3i3i300-1100002-22-2−i3i3−i3i3-11−i3i3i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ3222222222-2-2-1-2-2-1-1-1-1-1-1-1002-22-20011−i3−i3i3i311−i3−i3i3i300-110000-22-22−i3i3−i3i3-11i3−i3−i3i3i3−i3−i3i31-11-11-11-10000000000000000
χ3322222222-2-2-1-2-2-1-1-1-1-1-1-1002-22-20011i3i3−i3−i311i3i3−i3−i300-1100002-22-2i3−i3i3−i3-11i3−i3−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ3422222222-2-2-1-2-2-1-1-1-1-1-1-1002-22-20011i3i3−i3−i311i3i3−i3−i300-110000-22-22i3−i3i3−i3-11−i3i3i3−i3−i3i3i3−i31-11-11-11-10000000000000000
χ3522222222-2-2-1-2-2-1-1-1-1-1-1-100-22-220011−i3−i3i3i311−i3−i3i3i3001-12-22-20000i3−i3i3−i31-1-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ3622222222-2-2-1-2-2-1-1-1-1-1-1-100-22-220011−i3−i3i3i311−i3−i3i3i3001-1-22-220000i3−i3i3−i31-11-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ3722222222-2-2-1-2-2-1-1-1-1-1-1-100-22-220011i3i3−i3−i311i3i3−i3−i3001-12-22-20000−i3i3−i3i31-1-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ3822222222-2-2-1-2-2-1-1-1-1-1-1-100-22-220011i3i3−i3−i311i3i3−i3−i3001-1-22-220000−i3i3−i3i31-11-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ392222-2-2-2-2222-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-222200000000-2-222-2-200000000000000000000000000000000
χ402222-2-2-2-2222-2-2222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2220000000022-2-2-2-200000000000000000000000000000000
χ412222-2-2-2-222-1-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-10000000011-1-11133−3−3−3−33333−3−3−3−3330000000000000000
χ422222-2-2-2-222-1-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22-1-10000000011-1-111−3−33333−3−3−3−33333−3−30000000000000000
χ432222-2-2-2-222-1-2-2-1-1-1111122-2-222-2-2-1-1-1-1-1-11111112-2112i2i−2i−2i2i2i−2i−2i-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ442222-2-2-2-222-1-2-2-1-1-1111122-2-222-2-2-1-1-1-1-1-11111112-211−2i−2i2i2i−2i−2i2i2i-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ452222-2-2-2-222-1-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-2-1-100000000-1-1111133−3−3−3−333−3−33333−3−30000000000000000
χ462222-2-2-2-222-1-2-2-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-2-1-100000000-1-11111−3−33333−3−333−3−3−3−3330000000000000000
χ472222-2-2-2-222-1-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22112i2i−2i−2i−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ482222-2-2-2-222-1-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-2211−2i−2i2i2i2i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ492222-2-2-2-2-2-2222222-2-2-2-2002-2-2200-2-20000220000002-22i−2i−2i2i00000000-222i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ502222-2-2-2-2-2-2222222-2-2-2-2002-2-2200-2-20000220000002-2−2i2i2i−2i00000000-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ512222-2-2-2-2-2-2222222-2-2-2-200-222-200-2-2000022000000-2200002i−2i−2i2i00002-2000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ522222-2-2-2-2-2-2222222-2-2-2-200-222-200-2-2000022000000-220000−2i2i2i−2i00002-200000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ532222-2-2-2-2-2-2-122-1-1-11111002-2-220011−i3−i3i3i3-1-1i3i3−i3−i300-112i−2i−2i2i0000i3−i3−i3i31-1−ii−iii−ii−i3−3−33−333−30000000000000000
χ542222-2-2-2-2-2-2-122-1-1-11111002-2-220011−i3−i3i3i3-1-1i3i3−i3−i300-11−2i2i2i−2i0000i3−i3−i3i31-1i−ii−i−ii−ii−333−33−3−330000000000000000
χ552222-2-2-2-2-2-2-122-1-1-11111002-2-220011i3i3−i3−i3-1-1−i3−i3i3i300-112i−2i−2i2i0000−i3i3i3−i31-1−ii−iii−ii−i−333−33−3−330000000000000000
χ562222-2-2-2-2-2-2-122-1-1-11111002-2-220011i3i3−i3−i3-1-1−i3−i3i3i300-11−2i2i2i−2i0000−i3i3i3−i31-1i−ii−i−ii−ii3−3−33−333−30000000000000000
χ572222-2-2-2-2-2-2-122-1-1-1111100-222-20011−i3−i3i3i3-1-1i3i3−i3−i3001-100002i−2i−2i2i−i3i3i3−i3-113−3−33−333−3−ii−iii−ii−i0000000000000000
χ582222-2-2-2-2-2-2-122-1-1-1111100-222-20011−i3−i3i3i3-1-1i3i3−i3−i3001-10000−2i2i2i−2i−i3i3i3−i3-11−333−33−3−33i−ii−i−ii−ii0000000000000000
χ592222-2-2-2-2-2-2-122-1-1-1111100-222-20011i3i3−i3−i3-1-1−i3−i3i3i3001-100002i−2i−2i2ii3−i3−i3i3-11−333−33−3−33−ii−iii−ii−i0000000000000000
χ602222-2-2-2-2-2-2-122-1-1-1111100-222-20011i3i3−i3−i3-1-1−i3−i3i3i3001-10000−2i2i2i−2ii3−i3−i3i3-113−3−33−333−3i−ii−i−ii−ii0000000000000000
χ612-22-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i2-200002i−2i2-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ622-22-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i2-200002i−2i2-22-22-22i−2i2i−2i2i−2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ632-22-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i-220000−2i2i2-2-22-222i−2i−2i2i−2i2i0000000000000000000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ642-22-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i-220000−2i2i2-2-22-222i−2i−2i2i−2i2i000000000000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ652-22-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i2-20000−2i2i2-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ662-22-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i2-20000−2i2i2-22-22-2−2i2i−2i2i−2i2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ672-22-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i-2200002i−2i2-2-22-22−2i2i2i−2i2i−2i0000000000000000000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ682-22-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i-2200002i−2i2-2-22-22−2i2i2i−2i2i−2i000000000000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ6944-4-44-44-400400-4-444-44-40000000000000000000000000000000000000000000000000000002i−2i2i−2i000000000000
χ7044-4-44-44-400400-4-444-44-4000000000000000000000000000000000000000000000000000000−2i2i−2i2i000000000000
χ7144-4-4-44-4400400-4-44-44-440000000000000000000000000000000000000000000000000000002i−2i−2i2i000000000000
χ7244-4-4-44-4400400-4-44-44-44000000000000000000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ734-44-44i4i−4i−4i4-4-24i−4i-222−2i−2i2i2i4-400004i−4i-22-22-22−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ744-44-44i4i−4i−4i4-4-24i−4i-222−2i−2i2i2i-440000−4i4i-222-22-2−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ754-44-44i4i−4i−4i-444−4i4i4-4-44i4i−4i−4i00000000-440000−4i4i000000000000000000000000000000000000000000000000000000
χ764-44-44i4i−4i−4i-44-2−4i4i-222−2i−2i2i2i000000002-2−2i32i32i3−2i32i−2i23−23−232300000000000000000000000000000000000000000000000000
χ774-44-44i4i−4i−4i-44-2−4i4i-222−2i−2i2i2i000000002-22i3−2i3−2i32i32i−2i−232323−2300000000000000000000000000000000000000000000000000
χ784-44-4−4i−4i4i4i4-4-2−4i4i-2222i2i−2i−2i4-40000−4i4i-22-22-222i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ794-44-4−4i−4i4i4i4-4-2−4i4i-2222i2i−2i−2i-4400004i−4i-222-22-22i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ804-44-4−4i−4i4i4i-4444i−4i4-4-4−4i−4i4i4i00000000-4400004i−4i000000000000000000000000000000000000000000000000000000
χ814-44-4−4i−4i4i4i-44-24i−4i-2222i2i−2i−2i000000002-2−2i32i32i3−2i3−2i2i−232323−2300000000000000000000000000000000000000000000000000
χ824-44-4−4i−4i4i4i-44-24i−4i-2222i2i−2i−2i000000002-22i3−2i3−2i32i3−2i2i23−23−232300000000000000000000000000000000000000000000000000
χ834-4-444i−4i−4i4i00400-44-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000002i−2i2-200000000
χ844-4-444i−4i−4i4i00400-44-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000−2i2i-2200000000
χ854-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000002i−2i-2200000000
χ864-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000−2i2i2-200000000
χ8788-8-88-88-800-40044-4-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-88-8800-40044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-888i−8i−8i8i00-4004-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88−8i8i8i−8i00-4004-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000

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