Finite Group Databasebeta

← Group #11785495

Character table — Group #11785495

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222222222444444444444444444444444444444666666666666888888888888888812121212121212121212121212121212121224242424242424242424242472727272
order1244222334446666121212121212223446666666666661212121212121212121212121288882424242424242424666666661212121212121212888888242424242424242424242424444412121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-1111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ911111-1-111-1-1111111111111-111-11-1-111-1-1111-1-11-1-1-1-111-1-111111111111111111-1-1-111-1-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ1011111-1-111-1-1111111111111-111-11-1-111-1-1111-1-11-1-1-1-111-1-111111111111111111-1-1-111-1-11-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ1111111-1-111-1-1111111111111-111-11-1-111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11-1-1-111-1-111-1-1111111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ1211111-1-111-1-1111111111111-111-11-1-111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11-1-1-111-1-111-1-1111111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ1311111-1-111-1-111111111111-111-111-1-1-1-111111-1-11-1-1-1-1-1-1111111111111111111-11-1-1-1-111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ1411111-1-111-1-111111111111-111-111-1-1-1-111111-1-11-1-1-1-1-1-1111111111111111111-11-1-1-1-111-11-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ1511111-1-111-1-111111111111-111-111-1-1-1-111111-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-11-1-1-1-1111111-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ1611111-1-111-1-111111111111-111-111-1-1-1-111111-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-11-1-1-1-1111111-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ1722222222-1222222-122-1-12222-122-1222222-1-1-1-1-1-122-1-12222-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-1-1-1-10000
χ1822222222-1222222-122-1-12222-122-1222222-1-1-1-1-1-122-1-12222-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2111111110000
χ1922222222-1222222-122-1-122-2-2-1-2-2-122-2-2-2-2-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-100000000000011-1-1111111-1-1111100000000000000000022-2-2-1-1-1-111110000
χ2022222222-1222222-122-1-122-2-2-1-2-2-122-2-2-2-2-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-100000000000011-1-1111111-1-11111000000000000000000-2-2221111-1-1-1-10000
χ212222222-12222-1-1-12-1-122-1-122-1222-1-1-1-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ222222222-12222-1-1-12-1-122-1-122-1222-1-1-1-1-1-1-1-1-1222-1-122-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-21111111111110000000000000000
χ232222222-12222-1-1-12-1-122-1-1-2-2-1-2-22-1-11111-1-1-1222-1-1221111-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-1-11111-2-2-1-1111122-2-2-2-2-1-1-1-1111111110000000000000000
χ242222222-12222-1-1-12-1-122-1-1-2-2-1-2-22-1-11111-1-1-1222-1-1221111-1-1-1-1-2-2-2-211111111-2-2-1-11111-2-2-1-11111-2-222221111-1-1-1-1-1-1-1-10000000000000000
χ2522222-2-22-1-2-22222-122-1-1222-2-12-2-1-2-222-2-2-1-1-111-1-2-21122-2-2-1-1-1-1000000000000-1111-1-111-1111-1-1110000000000000000002i−2i2i−2i−i−iii−i−iii0000
χ2622222-2-22-1-2-22222-122-1-1222-2-12-2-1-2-222-2-2-1-1-111-1-2-21122-2-2-1-1-1-1000000000000-1111-1-111-1111-1-111000000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ2722222-2-22-1-2-22222-122-1-122-22-1-22-1-2-2-2-222-1-1-111-1-2-211-2-222-1-1-1-10000000000001-11111-1-11-11111-1-10000000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ2822222-2-22-1-2-22222-122-1-122-22-1-22-1-2-2-2-222-1-1-111-1-2-211-2-222-1-1-1-10000000000001-11111-1-11-11111-1-1000000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ2922222-2-2-12-2-22-1-1-12-1-122-1-12-2-12-2211-1-111-1-1-1-2-2211-2-2-1-111-1-1-1-12222-1-1-1-1-1-1-1-12-211-1-1112-211-1-111-2-222-2-21111-1-1-1-111110000000000000000
χ3022222-2-2-12-2-22-1-1-12-1-122-1-12-2-12-2211-1-111-1-1-1-2-2211-2-2-1-111-1-1-1-1-2-2-2-2111111112-211-1-1112-211-1-11122-2-222-1-1-1-11111-1-1-1-10000000000000000
χ3122222-2-2-12-2-22-1-1-12-1-122-1-1-22-1-2221111-1-1-1-1-1-2-2211-2-211-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-221111-1-1-221111-1-1-2-2-2-22211111111-1-1-1-10000000000000000
χ3222222-2-2-12-2-22-1-1-12-1-122-1-1-22-1-2221111-1-1-1-1-1-2-2211-2-211-1-1-1-1-1-1-2-2-2-211111111-221111-1-1-221111-1-12222-2-2-1-1-1-1-1-1-1-111110000000000000000
χ332222-22-2222-2-2-2-2222222-2-200200-22-20000-2-222-2-22-22-2000022-2-2000000000000002-20000002-20000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i0000000000000000
χ342222-22-2222-2-2-2-2222222-2-200200-22-20000-2-222-2-22-22-2000022-2-2000000000000002-20000002-2000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ352222-22-2-122-2-211-12-1-1221100-100-2-11−i3i3−i3i311-12-2-2-112-2−i3i3−i3i3-1-11100003333−3−3−3−300-11−i3i3−i3i300-11−i3i3−i3i3002i−2i2i−2i33−3−3−i−iii−i−iii0000000000000000
χ362222-22-2-122-2-211-12-1-1221100-100-2-11−i3i3−i3i311-12-2-2-112-2−i3i3−i3i3-1-1110000−3−3−3−3333300-11−i3i3−i3i300-11−i3i3−i3i300−2i2i−2i2i−3−333ii−i−iii−i−i0000000000000000
χ372222-22-2-122-2-211-12-1-1221100-100-2-11i3−i3i3−i311-12-2-2-112-2i3−i3i3−i3-1-11100003333−3−3−3−300-11i3−i3i3−i300-11i3−i3i3−i300−2i2i−2i2i33−3−3ii−i−iii−i−i0000000000000000
χ382222-22-2-122-2-211-12-1-1221100-100-2-11i3−i3i3−i311-12-2-2-112-2i3−i3i3−i3-1-1110000−3−3−3−3333300-11i3−i3i3−i300-11i3−i3i3−i3002i−2i2i−2i−3−333−i−iii−i−iii0000000000000000
χ392222-2-2222-22-2-2-2222222-2-200200-2-220000-2-22-22-2-22-22000022-2-200000000000000-22000000-220000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2222-22-2-2-2222222-2-200200-2-220000-2-22-22-2-22-22000022-2-200000000000000-22000000-22000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-22-12-22-211-12-1-1221100-100-21-1−i3i3i3−i311-1-22-21-1-22−i3i3i3−i3-1-11100003333−3−3−3−3001-1−i3i3i3−i3001-1−i3i3i3−i3002i−2i−2i2i−3−333−i−iiiii−i−i0000000000000000
χ422222-2-22-12-22-211-12-1-1221100-100-21-1−i3i3i3−i311-1-22-21-1-22−i3i3i3−i3-1-1110000−3−3−3−33333001-1−i3i3i3−i3001-1−i3i3i3−i300−2i2i2i−2i33−3−3ii−i−i−i−iii0000000000000000
χ432222-2-22-12-22-211-12-1-1221100-100-21-1i3−i3−i3i311-1-22-21-1-22i3−i3−i3i3-1-11100003333−3−3−3−3001-1i3−i3−i3i3001-1i3−i3−i3i300−2i2i2i−2i−3−333ii−i−i−i−iii0000000000000000
χ442222-2-22-12-22-211-12-1-1221100-100-21-1i3−i3−i3i311-1-22-21-1-22i3−i3−i3i3-1-1110000−3−3−3−33333001-1i3−i3−i3i3001-1i3−i3−i3i3002i−2i−2i2i33−3−3−i−iiiii−i−i0000000000000000
χ4522-2-222222-2-2-22222-2-2-2-2-2-22-22-2222222-2-222222-2-2-2-2-2-2-222-2-2-2-20000000000002-22222-2-2-22-2-2-2-2220000000000000000000000000000000000
χ4622-2-222222-2-2-22222-2-2-2-2-2-2-2222-2222-2-22222222-2-2-2-2-222-2-2-2-2-2-2000000000000-2222-2-2222-2-2-222-2-20000000000000000000000000000000000
χ4722-2-22222-1-2-2-2222-1-2-211-2-22-2-1-22-12222-2-2-1-1-1-1-11-2-211-2-2221111000000000000-11-1-1-1-1111-11111-1-10000000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ4822-2-22222-1-2-2-2222-1-2-211-2-22-2-1-22-12222-2-2-1-1-1-1-11-2-211-2-2221111000000000000-11-1-1-1-1111-11111-1-10000000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ4922-2-22222-1-2-2-2222-1-2-211-2-2-22-12-2-122-2-222-1-1-1-1-11-2-21122-2-211110000000000001-1-1-111-1-1-1111-1-1110000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ5022-2-22222-1-2-2-2222-1-2-211-2-2-22-12-2-122-2-222-1-1-1-1-11-2-21122-2-211110000000000001-1-1-111-1-1-1111-1-1110000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ5122-2-2222-12-2-2-2-1-1-1211-2-2112-2-1-222-1-1-1-111-1-1-122-211-2-211-1-11111000033−3−333−3−32-2-1-1-1-111-221111-1-10000003−33−33−33−33−33−30000000000000000
χ5222-2-2222-12-2-2-2-1-1-1211-2-2112-2-1-222-1-1-1-111-1-1-122-211-2-211-1-111110000−3−333−3−3332-2-1-1-1-111-221111-1-1000000−33−33−33−33−33−330000000000000000
χ5322-2-2222-12-2-2-2-1-1-1211-2-211-22-12-22-1-111-1-1-1-1-122-211-2-2-1-1111111000033−3−333−3−3-22-1-111-1-12-211-1-1110000003−33−3−33−33−33−330000000000000000
χ5422-2-2222-12-2-2-2-1-1-1211-2-211-22-12-22-1-111-1-1-1-1-122-211-2-2-1-11111110000−3−333−3−333-22-1-111-1-12-211-1-111000000−33−333−33−33−33−30000000000000000
χ5522-2-22-2-22222-22222-2-2-2-2-2-2222-2-22-2-22222222-2-2-22222-2-2-2-2-2-2-2-200000000000022-2-22222-2-222-2-2-2-20000000000000000000000000000000000
χ5622-2-22-2-22222-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2222-2-2-222222222-2-2-2-2000000000000-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000
χ5722-2-22-2-22-122-2222-1-2-211-2-222-1-2-2-1-2-22222-1-1-111122-1-1-2-2-2-21111000000000000-1-111-1-1-1-111-1-1111100000000000000000000003−3−333−3−330000
χ5822-2-22-2-22-122-2222-1-2-211-2-222-1-2-2-1-2-22222-1-1-111122-1-1-2-2-2-21111000000000000-1-111-1-1-1-111-1-111110000000000000000000000−333−3−333−30000
χ5922-2-22-2-22-122-2222-1-2-211-2-2-2-2-122-1-2-2-2-2-2-2-1-1-111122-1-12222111100000000000011111111-1-1-1-1-1-1-1-100000000000000000000003−3−33−333−30000
χ6022-2-22-2-22-122-2222-1-2-211-2-2-2-2-122-1-2-2-2-2-2-2-1-1-111122-1-12222111100000000000011111111-1-1-1-1-1-1-1-10000000000000000000000−333−33−3−330000
χ6122-2-22-2-2-1222-2-1-1-1211-2-21122-1-2-2211-1-1-1-1-1-1-1-2-2-2-1-12211111111000033−3−333−3−32211-1-1-1-1-2-2-1-11111000000−33−333−33−3−33−330000000000000000
χ6222-2-22-2-2-1222-2-1-1-1211-2-21122-1-2-2211-1-1-1-1-1-1-1-2-2-2-1-122111111110000−3−333−3−3332211-1-1-1-1-2-2-1-111110000003−33−3−33−333−33−30000000000000000
χ6322-2-22-2-2-1222-2-1-1-1211-2-211-2-2-1222111111-1-1-1-2-2-2-1-122-1-1-1-11111000033−3−333−3−3-2-211111122-1-1-1-1-1-1000000−33−33−33−333−33−30000000000000000
χ6422-2-22-2-2-1222-2-1-1-1211-2-211-2-2-1222111111-1-1-1-2-2-2-1-122-1-1-1-111110000−3−333−3−333-2-211111122-1-1-1-1-1-10000003−33−33−33−3−33−330000000000000000
χ6522-2-2-22-222-222-2-222-2-2-2-22200200-22-20000-2-222-22-22-220000-2-22222-2-222-2-2-2-222002-2000000-2200002-200002-2-22000000000000000000000000
χ6622-2-2-22-222-222-2-222-2-2-2-22200200-22-20000-2-222-22-22-220000-2-222-2-222-2-22222-2-2002-2000000-220000-220000-222-2000000000000000000000000
χ6722-2-2-22-2-12-22211-1211-2-2-1-100-100-2-11−i3i3i3−i311-12-221-1-22i3−i3−i3i311-1-122-2-2-1-11111-1-100-11−i3i3i3−i3001-1i3−i3−i3i32-20000-111-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ6822-2-2-22-2-12-22211-1211-2-2-1-100-100-2-11−i3i3i3−i311-12-221-1-22i3−i3−i3i311-1-1-2-22211-1-1-1-11100-11−i3i3i3−i3001-1i3−i3−i3i3-2200001-1-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ6922-2-2-22-2-12-22211-1211-2-2-1-100-100-2-11i3−i3−i3i311-12-221-1-22−i3i3i3−i311-1-122-2-2-1-11111-1-100-11i3−i3−i3i3001-1−i3i3i3−i32-20000-111-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ7022-2-2-22-2-12-22211-1211-2-2-1-100-100-2-11i3−i3−i3i311-12-221-1-22−i3i3i3−i311-1-1-2-22211-1-1-1-11100-11i3−i3−i3i3001-1−i3i3i3−i3-2200001-1-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ7122-2-2-2-22222-22-2-222-2-2-2-22200200-2-220000-2-22-2222-22-20000-2-22222-2-222-2-2-2-22200-220000002-20000-220000-222-2000000000000000000000000
χ7222-2-2-2-22222-22-2-222-2-2-2-22200200-2-220000-2-22-2222-22-20000-2-222-2-222-2-22222-2-200-220000002-200002-200002-2-22000000000000000000000000
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χ1098-88i−8i0008-400000-848i−8i−4i4i0000-400000000000400000000000−4i4i0000000000000000000000000000000000000000000000000000000000000000
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χ1128-8−8i8i0008-400000-84−8i8i4i−4i0000-4000000000004000000000004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1138-8−8i8i000-4-4000−4i34i3444i−4i4i−4i−43430020000000002i3−2i3-200000000000−2i2i23−2300000000000000000000000000000000000000000000000000000000000000
χ1148-8−8i8i000-4-40004i3−4i3444i−4i4i−4i43−43002000000000−2i32i3-200000000000−2i2i−232300000000000000000000000000000000000000000000000000000000000000

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