Finite Group Databasebeta

← Group #10691592

Character table — Group #10691592

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222234444446661212121222444446666668888121212121212121212122424242424242424246688888812121212242424242424242424242424888888882288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-111-1-1111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-111-1-1111-1-1-1-11111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-11-1111-1-1-1-1111-1-1-1-1111111ii−i−i11-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111i−iii−i−i1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ1011111111-1-1-11-1111-1-1-1-1111-1-1-1-1111111ii−i−i11-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111i−iii−i−i1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ1111111111-1-1-11-1111-1-1-1-1111-1-1-1-1111111−i−iii11-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111−ii−i−iii1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ1211111111-1-1-11-1111-1-1-1-1111-1-1-1-1111111−i−iii11-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111−ii−i−iii1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ1311111111-1-1-11-1111-1-1-1-1-1-11-111-111-1-1-1-1ii−i−i11-1-1-1-11111iiii−i−i−i−i-11-1-1i−i−i−iii1-111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ1411111111-1-1-11-1111-1-1-1-1-1-11-111-111-1-1-1-1ii−i−i11-1-1-1-11111iiii−i−i−i−i-11-1-1i−i−i−iii1-111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ1511111111-1-1-11-1111-1-1-1-1-1-11-111-111-1-1-1-1−i−iii11-1-1-1-11111−i−i−i−iiiii-11-1-1−iiii−i−i1-111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ1611111111-1-1-11-1111-1-1-1-1-1-11-111-111-1-1-1-1−i−iii11-1-1-1-11111−i−i−i−iiiii-11-1-1−iiii−i−i1-111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222-2222-22222222200-2-200-22200002222-2-2-2-2220000222222220000-2-20000-2-200-2-2-2-200000000000000000000
χ182222222-2222-22222222200-2-200-2220000-2-2-2-2-2-2-2-2220000-2-2-2-2-2-2-2-20000220000-2-200222200000000000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-200-220022200002i2i−2i−2i-2-222-2-200002i2i2i2i−2i−2i−2i−2i0000−2i2i0000-2200−2i−2i2i2i00000000000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-200-22002220000−2i−2i2i2i-2-222-2-20000−2i−2i−2i−2i2i2i2i2i00002i−2i0000-22002i2i−2i−2i00000000000000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111122-1-1-2-2-2-2-2-2-1-1-1-1111111111111000000000000
χ23222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-111112222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-21122-2-2-2-2-1-111-1-1-1-111111111000000000000
χ24222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-11111-2-2-2-2-1-1-1-1-1-1111111111111-2-211-2-22222-1-1111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12-2-2-22-2-1-1-11111222-2-2-2-2-1-1-1-1-1-12i2i−2i−2i-1-111111111−i−i−i−iiiii2-2-1-12i−2i2i2i−2i−2i-1111−i−iii−i−i−i−iiiii000000000000
χ26222222-12-2-2-22-2-1-1-11111222-2-2-2-2-1-1-1-1-1-1−2i−2i2i2i-1-111111111iiii−i−i−i−i2-2-1-1−2i2i−2i−2i2i2i-1111ii−i−iiiii−i−i−i−i000000000000
χ27222222-12-2-2-22-2-1-1-11111-2-22-222-2-1-111112i2i−2i−2i-1-11111-1-1-1-1−i−i−i−iiiii-22112i−2i−2i−2i2i2i-11-1-1−i−iiiiiii−i−i−i−i000000000000
χ28222222-12-2-2-22-2-1-1-11111-2-22-222-2-1-11111−2i−2i2i2i-1-11111-1-1-1-1iiii−i−i−i−i-2211−2i2i2i2i−2i−2i-11-1-1ii−i−i−i−i−i−iiiii000000000000
χ29222222-1-2222-22-1-1-1-1-1-1-100-2-200-2-1-1−i3−i3i3i322221111-1-1−i3−i3i3i3-1-1-1-1-1-1-1-100−i3i3-2-2000011−i3i31111−i3−i3i3i3−i3−i3i3i3000000000000
χ30222222-1-2222-22-1-1-1-1-1-1-100-2-200-2-1-1−i3−i3i3i3-2-2-2-21111-1-1−i3−i3i3i31111111100−i3i322000011−i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ31222222-1-2222-22-1-1-1-1-1-1-100-2-200-2-1-1i3i3−i3−i322221111-1-1i3i3−i3−i3-1-1-1-1-1-1-1-100i3−i3-2-2000011i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000
χ32222222-1-2222-22-1-1-1-1-1-1-100-2-200-2-1-1i3i3−i3−i3-2-2-2-21111-1-1i3i3−i3−i31111111100i3−i322000011i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ33222222-1-2-2-2-2-2-2-1-1-1111100-22002-1-1−i3−i3i3i32i2i−2i−2i11-1-111i3i3−i3−i3−i−i−i−iiiii00−i3i3−2i2i00001-1i3−i3ii−i−i33−3−3−3−333000000000000
χ34222222-1-2-2-2-2-2-2-1-1-1111100-22002-1-1−i3−i3i3i3−2i−2i2i2i11-1-111i3i3−i3−i3iiii−i−i−i−i00−i3i32i−2i00001-1i3−i3−i−iii−3−33333−3−3000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1111100-22002-1-1i3i3−i3−i32i2i−2i−2i11-1-111−i3−i3i3i3−i−i−i−iiiii00i3−i3−2i2i00001-1−i3i3ii−i−i−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1111100-22002-1-1i3i3−i3−i3−2i−2i2i2i11-1-111−i3−i3i3i3iiii−i−i−i−i00i3−i32i−2i00001-1−i3i3−i−iii33−3−3−3−333000000000000
χ372222-2-2222-2-222222-2-2-2-222-2-2-2-22-2-22222000022-2-222-2-2-2-200000000-22-2-2000000-2222000000000000000000000000
χ382222-2-2222-2-222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2000022-2-2222222000000002-222000000-22-2-2000000000000000000000000
χ392222-2-222-2222-2222222222-2222-2-2-2222200002222-2-2222200000000-2-2-2-2000000-2-2-2-2000000000000000000000000
χ402222-2-222-2222-22222222-2-2-22-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2000000002222000000-2-222000000000000000000000000
χ412222-2-22-22-2-2-22222-2-2-2-2002200-2-2-200000000-2-222220000000000000000002i−2i2i−2i2-20000002i−2i2i−2i2i−2i2i−2i000000000000
χ422222-2-22-22-2-2-22222-2-2-2-2002200-2-2-200000000-2-22222000000000000000000−2i2i−2i2i2-2000000−2i2i−2i2i−2i2i−2i2i000000000000
χ432222-2-22-2-222-2-22222222002-2002-2-200000000-2-2-2-2-2-20000000000000000002-2-22220000002-22-2-22-22000000000000
χ442222-2-22-2-222-2-22222222002-2002-2-200000000-2-2-2-2-2-2000000000000000000-222-222000000-22-222-22-2000000000000
χ452222-2-2-122-2-222-1-1-1111122-2-2-2-2211-1-1-1-10000-1-111-1-1111133−3−333−3−3-22110000001-1-1-13−33−33−3−333−3−33000000000000
χ462222-2-2-122-2-222-1-1-1111122-2-2-2-2211-1-1-1-10000-1-111-1-11111−3−333−3−333-22110000001-1-1-1−33−33−333−3−333−3000000000000
χ472222-2-2-122-2-222-1-1-11111-2-2-2-22221111110000-1-111-1-1-1-1-1-133−3−333−3−32-2-1-10000001-1113−33−3−333−3−333−3000000000000
χ482222-2-2-122-2-222-1-1-11111-2-2-2-22221111110000-1-111-1-1-1-1-1-1−3−333−3−3332-2-1-10000001-111−33−333−3−333−3−33000000000000
χ492222-2-2-12-2222-2-1-1-1-1-1-1-122-2222-211-1-1-1-10000-1-1-1-111-1-1-1-1−i3−i3i3i3i3i3−i3−i3-2-2110000001111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ502222-2-2-12-2222-2-1-1-1-1-1-1-122-2222-211-1-1-1-10000-1-1-1-111-1-1-1-1i3i3−i3−i3−i3−i3i3i3-2-2110000001111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ512222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2-22-2-2-21111110000-1-1-1-1111111−i3−i3i3i3i3i3−i3−i322-1-100000011-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
χ522222-2-2-12-2222-2-1-1-1-1-1-1-1-2-2-22-2-2-21111110000-1-1-1-1111111i3i3−i3−i3−i3−i3i3i322-1-100000011-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ532222-2-2-1-22-2-2-22-1-1-11111002200-211−i3−i3i3i3000011-1-1-1-1i3i3−i3−i333−3−333−3−300i3−i3002i−2i2i−2i-11−i3i3−33−33−ii−ii−ii−ii000000000000
χ542222-2-2-1-22-2-2-22-1-1-11111002200-211−i3−i3i3i3000011-1-1-1-1i3i3−i3−i3−3−333−3−33300i3−i300−2i2i−2i2i-11−i3i33−33−3i−ii−ii−ii−i000000000000
χ552222-2-2-1-22-2-2-22-1-1-11111002200-211i3i3−i3−i3000011-1-1-1-1−i3−i3i3i333−3−333−3−300−i3i300−2i2i−2i2i-11i3−i3−33−33i−ii−ii−ii−i000000000000
χ562222-2-2-1-22-2-2-22-1-1-11111002200-211i3i3−i3−i3000011-1-1-1-1−i3−i3i3i3−3−333−3−33300−i3i3002i−2i2i−2i-11i3−i33−33−3−ii−ii−ii−ii000000000000
χ572222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211−i3−i3i3i30000111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300i3−i3002-2-22-1-1i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ582222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211−i3−i3i3i30000111111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300i3−i300-222-2-1-1i3−i3−i3i3i3−i31-11-1-11-11000000000000
χ592222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211i3i3−i3−i30000111111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300−i3i300-222-2-1-1−i3i3i3−i3−i3i31-11-1-11-11000000000000
χ602222-2-2-1-2-222-2-2-1-1-1-1-1-1-1002-200211i3i3−i3−i30000111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300−i3i3002-2-22-1-1−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ612-2-222-22022-20-2-2-2222-2-200000002-200002i−2i2i−2i00002-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000002−22−2−i2i2−i2i20000
χ622-2-222-22022-20-2-2-2222-2-200000002-200002i−2i2i−2i00002-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−22−22i2−i2i2−i20000
χ632-2-222-22022-20-2-2-2222-2-200000002-20000−2i2i−2i2i00002-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002−22−2i2−i2i2−i20000
χ642-2-222-22022-20-2-2-2222-2-200000002-20000−2i2i−2i2i00002-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−22−22−i2i2−i2i20000
χ652-2-222-220-2-2202-2-22-2-22200000002-200002-2-220000-2200002-22-2-22-22000000000000000000000000002−2−22−222−20000
χ662-2-222-220-2-2202-2-22-2-22200000002-200002-2-220000-2200002-22-2-22-2200000000000000000000000000−222−22−2−220000
χ672-2-222-220-2-2202-2-22-2-22200000002-20000-222-20000-220000-22-222-22-2000000000000000000000000002−2−222−2−220000
χ682-2-222-220-2-2202-2-22-2-22200000002-20000-222-20000-220000-22-222-22-200000000000000000000000000−222−2−222−20000
χ6944-4-40044000-404-4-4000000004i−4i000000000004-400004i−4i4i−4i0000000000000000000000000000000000000000000000
χ7044-4-40044000-404-4-400000000−4i4i000000000004-40000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ7144-4-4004-4000404-4-400004-400000004-44-40000-44000000000000000000000000000000000000000000000000000000
χ7244-4-4004-4000404-4-40000-440000000-44-440000-44000000000000000000000000000000000000000000000000000000
χ7344-4-400-24000-40-22223−2323−2300004i−4i000−2i32i32i3−2i30000-2223−2300−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7444-4-400-24000-40-22223−2323−230000−4i4i0002i3−2i3−2i32i30000-2223−23002i−2i2i−2i0000000000000000000000000000000000000000000000
χ7544-4-400-24000-40-222−2323−232300004i−4i0002i3−2i3−2i32i30000-22−232300−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7644-4-400-24000-40-222−2323−23230000−4i4i000−2i32i32i3−2i30000-22−2323002i−2i2i−2i0000000000000000000000000000000000000000000000
χ7744-4-400-2-400040-22223−2323−234-40000000-22-2200002-2−23230023−23−23230000000000000000000000000000000000000000000000
χ7844-4-400-2-400040-22223−2323−23-4400000002-22-200002-2−232300−232323−230000000000000000000000000000000000000000000000
χ7944-4-400-2-400040-222−2323−23234-40000000-22-2200002-223−2300−232323−230000000000000000000000000000000000000000000000
χ8044-4-400-2-400040-222−2323−2323-4400000002-22-200002-223−230023−23−23230000000000000000000000000000000000000000000000
χ814-4-444-4-2044-40-422-2-2-2220000000-2200004i−4i4i−4i0000-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000
χ824-4-444-4-2044-40-422-2-2-2220000000-220000−4i4i−4i4i0000-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000
χ834-4-444-4-20-4-440422-222-2-20000000-2200004-4-4400002-20000-22-222-22-200000000000000000000000000000000000000
χ844-4-444-4-20-4-440422-222-2-20000000-220000-444-400002-200002-22-2-22-2200000000000000000000000000000000000000
χ854-4-44-44404-440-4-4-44-4-4440000000-440000000000004-400000000000000000000000000000000000000000000000000
χ864-4-44-4440-44-404-4-4444-4-40000000-44000000000000-4400000000000000000000000000000000000000000000000000
χ874-4-44-44-204-440-422-222-2-200000002-2000000000000-220000−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000
χ884-4-44-44-204-440-422-222-2-200000002-2000000000000-2200002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000
χ894-4-44-44-20-44-40422-2-2-22200000002-20000000000002-2000023−23−2323−232323−2300000000000000000000000000000000000000
χ904-4-44-44-20-44-40422-2-2-22200000002-20000000000002-20000−232323−2323−23−232300000000000000000000000000000000000000
χ918-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-88-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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