Finite Group Databasebeta

← Group #10849645

Character table — Group #10849645

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order122222344444444666121212121212121212121212444444444444446612121212121212121212121212121212121212121212246688881212121212122424242424242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ1211111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1111-11-1
χ1311111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222-222-2-2-2-2-22222222-2-2-2-2-2-2-2-22-200000000000022-2-222-2-2000000000000000000000000000000000000002-22-200000000
χ182222222-222-2-2-2-2-22222222-2-2-2-2-2-2-2-22-200000000000022-2-222-2-200000000000000000000000000000000000000-22-2200000000
χ192222222-2-2-222-2-2-2222-2-2-2-22222-2-2-2-2-2200000000000022-2-2-2-222000000000000000000000000000000000000002-2-2200000000
χ202222222-2-2-222-2-2-2222-2-2-2-22222-2-2-2-2-2200000000000022-2-2-2-22200000000000000000000000000000000000000-222-200000000
χ21222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ23222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2-2-211111111111111000000000000
χ24222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2112222111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12-2-2-2-2222-1-1-111111111-1-1-1-1-2-222222222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-21122-2-2-1-1-1-111-1-1-1-11111000000000000
χ26222222-12-2-2-2-2222-1-1-111111111-1-1-1-1-2-22222-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-211-2-222-1-1-1-1111111-1-1-1-1000000000000
χ27222222-12-2-2-2-2222-1-1-111111111-1-1-1-1-2-2-2-2-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111122-1-1-2-2221111-1-11111-1-1-1-1000000000000
χ28222222-12-2-2-2-2222-1-1-111111111-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-122-1-122-2-21111-1-1-1-1-1-11111000000000000
χ292222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-2222-2-200000000-2-222-2-22200000000000000002-222000022-2-2-2-200000000000000000000
χ302222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-2-22-2-22200000000-2-222-2-2220000000000000000-22-2-20000-2-2222200000000000000000000
χ312222-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22-222-2-200000000-2-22222-2-20000000000000000-22-2-2000022-2-22200000000000000000000
χ322222-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22-2-2-22200000000-2-22222-2-200000000000000002-2220000-2-222-2-200000000000000000000
χ332222-2-22-2222222-2222222222222222-2-2000000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000002-22-20000
χ342222-2-22-2222222-2222222222222222-2-2000000000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000-22-220000
χ352222-2-22-2-2-2-2-222-2222-2-2-2-2-2-2-2-2222222000000000000-2-2-2-222220000000000000000000000000000000000000000002-2-220000
χ362222-2-22-2-2-2-2-222-2222-2-2-2-2-2-2-2-2222222000000000000-2-2-2-22222000000000000000000000000000000000000000000-222-20000
χ372222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2222-2-20000000011-1-111-1-13333−3−3−3−33333−3−3−3−32-2-1-10000-1-1111133−3−333−3−3000000000000
χ382222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-2222-2-20000000011-1-111-1-1−3−3−3−33333−3−3−3−333332-2-1-10000-1-11111−3−333−3−333000000000000
χ392222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22-2-2220000000011-1-111-1-13333−3−3−3−33333−3−3−3−3-2211000011-1-1-1-1−3−333−3−333000000000000
χ402222-2-2-1222-2-2-2-22-1-1-1-1-1-1-111111111-22-2-2220000000011-1-111-1-1−3−3−3−33333−3−3−3−33333-2211000011-1-1-1-133−3−333−3−3000000000000
χ412222-2-2-12-2-222-2-22-1-1-11111-1-1-1-111112-222-2-20000000011-1-1-1-1113333−3−3−3−3−3−3−3−33333-22110000-1-111-1-133−3−3−3−333000000000000
χ422222-2-2-12-2-222-2-22-1-1-11111-1-1-1-111112-222-2-20000000011-1-1-1-111−3−3−3−333333333−3−3−3−3-22110000-1-111-1-1−3−33333−3−3000000000000
χ432222-2-2-12-2-222-2-22-1-1-11111-1-1-1-111112-2-2-2220000000011-1-1-1-1113333−3−3−3−3−3−3−3−333332-2-1-1000011-1-111−3−33333−3−3000000000000
χ442222-2-2-12-2-222-2-22-1-1-11111-1-1-1-111112-2-2-2220000000011-1-1-1-111−3−3−3−333333333−3−3−3−32-2-1-1000011-1-11133−3−3−3−333000000000000
χ4522-2-22-22-200002-222-2-20000000022-2-2002i−2i2i−2i00002i2i−2i−2i2-22-20000000000002i2i−2i−2i2i2i−2i−2i0000002-22i−2i2i−2i0000002-22-2000000000000
χ4622-2-22-22-200002-222-2-20000000022-2-2002i−2i2i−2i0000−2i−2i2i2i2-22-2000000000000−2i−2i2i2i−2i−2i2i2i000000-222i−2i2i−2i000000-22-22000000000000
χ4722-2-22-22-200002-222-2-20000000022-2-200−2i2i−2i2i00002i2i−2i−2i2-22-20000000000002i2i−2i−2i2i2i−2i−2i000000-22−2i2i−2i2i000000-22-22000000000000
χ4822-2-22-22-200002-222-2-20000000022-2-200−2i2i−2i2i0000−2i−2i2i2i2-22-2000000000000−2i−2i2i2i−2i−2i2i2i0000002-2−2i2i−2i2i0000002-22-2000000000000
χ4922-2-22-2-1-200002-22-11133−3−333−3−3-1-111002i−2i2i−2i00002i2i−2i−2i-11-113−33−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00−i3i3002-2−ii−ii−i3i33−33−3-11-11000000000000
χ5022-2-22-2-1-200002-22-11133−3−333−3−3-1-111002i−2i2i−2i0000−2i−2i2i2i-11-113−33−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00−i3i300-22−ii−ii−i3i3−33−331-11-1000000000000
χ5122-2-22-2-1-200002-22-11133−3−333−3−3-1-11100−2i2i−2i2i00002i2i−2i−2i-11-113−33−3−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii00i3−i300-22i−ii−ii3−i3−33−331-11-1000000000000
χ5222-2-22-2-1-200002-22-11133−3−333−3−3-1-11100−2i2i−2i2i0000−2i−2i2i2i-11-113−33−3i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i00i3−i3002-2i−ii−ii3−i33−33−3-11-11000000000000
χ5322-2-22-2-1-200002-22-111−3−333−3−333-1-111002i−2i2i−2i00002i2i−2i−2i-11-11−33−33i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00i3−i3002-2−ii−iii3−i3−33−33-11-11000000000000
χ5422-2-22-2-1-200002-22-111−3−333−3−333-1-111002i−2i2i−2i0000−2i−2i2i2i-11-11−33−33−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00i3−i300-22−ii−iii3−i33−33−31-11-1000000000000
χ5522-2-22-2-1-200002-22-111−3−333−3−333-1-11100−2i2i−2i2i00002i2i−2i−2i-11-11−33−33i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii00−i3i300-22i−ii−i−i3i33−33−31-11-1000000000000
χ5622-2-22-2-1-200002-22-111−3−333−3−333-1-11100−2i2i−2i2i0000−2i−2i2i2i-11-11−33−33−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i00−i3i3002-2i−ii−i−i3i3−33−33-11-11000000000000
χ5722-2-2-222-20000-2222-2-200000000-2-222002i−2i−2i2i2i2i−2i−2i0000-222-200002i2i−2i−2i−2i−2i2i2i0000000000002-2002i−2i−2i2i00-222-20000000000000000
χ5822-2-2-222-20000-2222-2-200000000-2-222002i−2i−2i2i−2i−2i2i2i0000-222-20000−2i−2i2i2i2i2i−2i−2i000000000000-22002i−2i−2i2i002-2-220000000000000000
χ5922-2-2-222-20000-2222-2-200000000-2-22200−2i2i2i−2i2i2i−2i−2i0000-222-200002i2i−2i−2i−2i−2i2i2i000000000000-2200−2i2i2i−2i002-2-220000000000000000
χ6022-2-2-222-20000-2222-2-200000000-2-22200−2i2i2i−2i−2i−2i2i2i0000-222-20000−2i−2i2i2i2i2i−2i−2i0000000000002-200−2i2i2i−2i00-222-20000000000000000
χ6122-2-2-22-1-20000-222-11133−3−3−3−33311-1-1002i−2i−2i2i2i2i−2i−2i00001-1-11−333−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300−i3i32-200−iii−ii3−i31-1-113−3−33000000000000
χ6222-2-2-22-1-20000-222-11133−3−3−3−33311-1-1002i−2i−2i2i−2i−2i2i2i00001-1-11−333−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300−i3i3-2200−iii−ii3−i3-111-1−333−3000000000000
χ6322-2-2-22-1-20000-222-11133−3−3−3−33311-1-100−2i2i2i−2i2i2i−2i−2i00001-1-11−333−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300i3−i3-2200i−i−ii−i3i3-111-1−333−3000000000000
χ6422-2-2-22-1-20000-222-11133−3−3−3−33311-1-100−2i2i2i−2i−2i−2i2i2i00001-1-11−333−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300i3−i32-200i−i−ii−i3i31-1-113−3−33000000000000
χ6522-2-2-22-1-20000-222-111−3−33333−3−311-1-1002i−2i−2i2i2i2i−2i−2i00001-1-113−3−33−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300i3−i32-200−iii−i−i3i31-1-11−333−3000000000000
χ6622-2-2-22-1-20000-222-111−3−33333−3−311-1-1002i−2i−2i2i−2i−2i2i2i00001-1-113−3−33ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300i3−i3-2200−iii−i−i3i3-111-13−3−33000000000000
χ6722-2-2-22-1-20000-222-111−3−33333−3−311-1-100−2i2i2i−2i2i2i−2i−2i00001-1-113−3−33−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300−i3i3-2200i−i−iii3−i3-111-13−3−33000000000000
χ6822-2-2-22-1-20000-222-111−3−33333−3−311-1-100−2i2i2i−2i−2i−2i2i2i00001-1-113−3−33ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300−i3i32-200i−i−iii3−i31-1-11−333−3000000000000
χ69444444-2-444-4-4-4-4-4-2-2-2-2-2-2-2222222224-4000000000000-2-222-2-22200000000000000000000000000000000000000000000000000
χ70444444-2-4-4-444-4-4-4-2-2-22222-2-2-2-22222-44000000000000-2-22222-2-200000000000000000000000000000000000000000000000000
χ714444-4-4-2-4444444-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-40000000000002222222200000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4-4-4-444-4-2-2-222222222-2-2-2-2440000000000002222-2-2-2-200000000000000000000000000000000000000000000000000
χ7344-4-44-4440000-44-44-4-400000000-4-444000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ7444-4-44-4-240000-44-4-2222323−23−23−23−23232322-2-200000000000000-222-223−23−232300000000000000000000000000000000000000000000000000
χ7544-4-44-4-240000-44-4-222−23−2323232323−23−2322-2-200000000000000-222-2−232323−2300000000000000000000000000000000000000000000000000
χ7644-4-4-444400004-4-44-4-40000000044-4-400000000000000-44-44000000000000000000000000000000000000000000000000000000
χ7744-4-4-44-2400004-4-4-2222323−23−232323−23−23-2-222000000000000002-22-2−2323−232300000000000000000000000000000000000000000000000000
χ7844-4-4-44-2400004-4-4-222−23−232323−23−232323-2-222000000000000002-22-223−2323−2300000000000000000000000000000000000000000000000000
χ794-44-40040004i−4i000-44-400004i−4i4i−4i00000000002-22-22i−2i2i−2i000000002-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ804-44-40040004i−4i000-44-400004i−4i4i−4i0000000000-22-22−2i2i−2i2i00000000-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ814-44-4004000−4i4i000-44-40000−4i4i−4i4i00000000002-22-2−2i2i−2i2i000000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ824-44-4004000−4i4i000-44-40000−4i4i−4i4i0000000000-22-222i−2i2i−2i00000000-22-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ834-44-400-20004i−4i0002-22−2i32i3−2i32i3−2i2i−2i2i23−2323−230000002-22-22i−2i2i−2i00000000−1+31−3−1+31−3−1−31+3−1−31+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.