Finite Group Databasebeta

← Group #11777862

Character table — Group #11777862

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order12224444888833666666121212121212121224242424242424244444888888888888888888884444888812121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−ii−ii-1-111-1-111−i−iii−i−iii
χ111111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii
χ121111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i-1-11111-1-1−i−iiiii−i−i
χ131111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-111-1-1−i−iii−i−iii
χ141111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11i−ii−i-1-111-1-111ii−i−iii−i−i
χ151111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222222222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ192222-2-2-2-22i2i−2i−2i22222222-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ202222-2-2-2-2−2i−2i2i2i22222222-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i0000000000000000000000000000000000000000
χ2122-2-222-2-22-22-22222-2-2-2-22222-2-2-2-222-2-222-2-20000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ2222-2-222-2-22-22-22222-2-2-2-22222-2-2-2-222-2-222-2-200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ2322-2-222-2-2-22-222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000022−2−222−2−2−2−222−2−222000000000000000000000000
χ2422-2-222-2-2-22-222222-2-2-2-22222-2-2-2-2-2-222-2-22200000000−2−222−2−22222−2−222−2−2000000000000000000000000
χ2522-2-2-2-2222i−2i−2i2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i0000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ2622-2-2-2-2222i−2i−2i2i2222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ2722-2-2-2-222−2i2i2i−2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i0000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ2822-2-2-2-222−2i2i2i−2i2222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i00000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ292-22-22i−2i2i−2i000022-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ302-22-22i−2i2i−2i000022-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ312-22-22i−2i2i−2i000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ322-22-22i−2i2i−2i000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ332-22-2−2i2i−2i2i000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ342-22-2−2i2i−2i2i000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ352-22-2−2i2i−2i2i000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ362-22-2−2i2i−2i2i000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ372-2-222i−2i−2i2i000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000002-22i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ382-2-222i−2i−2i2i000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000002-22i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ392-2-222i−2i−2i2i000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000-22−2i2i00002-2-22−2i2i2i−2i00000000000000000000000000000000
χ402-2-222i−2i−2i2i000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000-22−2i2i0000-222-22i−2i−2i2i00000000000000000000000000000000
χ412-2-22−2i2i2i−2i000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000002-2−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ422-2-22−2i2i2i−2i000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000002-2−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ432-2-22−2i2i2i−2i000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000-222i−2i00002-2-222i−2i−2i2i00000000000000000000000000000000
χ442-2-22−2i2i2i−2i000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000-222i−2i0000-222-2−2i2i2i−2i00000000000000000000000000000000
χ454444444444441-21-21-21-21-21-21-21-21-21-21-21-2000000000000000000000000002200220000-1-1-1-10000-1-1-1-1
χ464444444444441-21-21-21-21-21-21-21-21-21-21-21-200000000000000000000000000-2-200-2-20000111100001111
χ47444444444444-21-21-21-21-21-21-21-21-21-21-21-2100000000000000000000000022002200-1-1-1-10000-1-1-1-10000
χ48444444444444-21-21-21-21-21-21-21-21-21-21-21-21000000000000000000000000-2-200-2-2001111000011110000
χ4944444444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-12000000000000000000000000002200-2-20000-1-1-1-100001111
χ5044444444-4-4-4-41-21-21-21-21-21-21-21-2-12-12-12-1200000000000000000000000000-2-20022000011110000-1-1-1-1
χ5144444444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-10000000000000000000000002200-2-200-1-1-1-1000011110000
χ5244444444-4-4-4-4-21-21-21-21-21-21-21-212-12-12-12-1000000000000000000000000-2-200220011110000-1-1-1-10000
χ534444-4-4-4-44i4i−4i−4i1-21-21-21-2-12-12-12-12i−2ii−2i−i2i−i2i000000000000000000000000002-2002i−2i0000-1-1110000−i−iii
χ544444-4-4-4-44i4i−4i−4i1-21-21-21-2-12-12-12-12i−2ii−2i−i2i−i2i00000000000000000000000000-2200−2i2i000011-1-10000ii−i−i
χ554444-4-4-4-44i4i−4i−4i-21-21-21-212-12-12-12-1−2ii−2ii2i−i2i−i0000000000000000000000002-2002i−2i00-1-1110000−i−iii0000
χ564444-4-4-4-44i4i−4i−4i-21-21-21-212-12-12-12-1−2ii−2ii2i−i2i−i000000000000000000000000-2200−2i2i0011-1-10000ii−i−i0000
χ574444-4-4-4-4−4i−4i4i4i1-21-21-21-2-12-12-12-12−i2i−i2ii−2ii−2i000000000000000000000000002-200−2i2i0000-1-1110000ii−i−i
χ584444-4-4-4-4−4i−4i4i4i1-21-21-21-2-12-12-12-12−i2i−i2ii−2ii−2i00000000000000000000000000-22002i−2i000011-1-10000−i−iii
χ594444-4-4-4-4−4i−4i4i4i-21-21-21-212-12-12-12-12i−i2i−i−2ii−2ii0000000000000000000000002-200−2i2i00-1-1110000ii−i−i0000
χ604444-4-4-4-4−4i−4i4i4i-21-21-21-212-12-12-12-12i−i2i−i−2ii−2ii000000000000000000000000-22002i−2i0011-1-10000−i−iii0000
χ6144-4-444-4-44-44-41-21-2-12-121-21-2-12-121-2-121-2-120000000000000000000000000000000000003−33−300003−33−3
χ6244-4-444-4-44-44-41-21-2-12-121-21-2-12-121-2-121-2-12000000000000000000000000000000000000−33−330000−33−33
χ6344-4-444-4-44-44-4-21-212-12-1-21-212-12-1-212-1-212-1000000000000000000000000000000003−33−300003−33−30000
χ6444-4-444-4-44-44-4-21-212-12-1-21-212-12-1-212-1-212-100000000000000000000000000000000−33−330000−33−330000
χ6544-4-444-4-4-44-441-21-2-12-121-21-2-12-12-121-2-121-20000000000000000000000000000000000003−33−30000−33−33
χ6644-4-444-4-4-44-441-21-2-12-121-21-2-12-12-121-2-121-2000000000000000000000000000000000000−33−3300003−33−3
χ6744-4-444-4-4-44-44-21-212-12-1-21-212-12-12-1-212-1-21000000000000000000000000000000003−33−30000−33−330000
χ6844-4-444-4-4-44-44-21-212-12-1-21-212-12-12-1-212-1-2100000000000000000000000000000000−33−3300003−33−30000
χ6944-4-4-4-4444i−4i−4i4i1-21-2-12-12-12-121-21-2i−2i−i2i−i2ii−2i0000000000000000000000000000000000003−3−330000i3−i3−i3i3
χ7044-4-4-4-4444i−4i−4i4i1-21-2-12-12-12-121-21-2i−2i−i2i−i2ii−2i000000000000000000000000000000000000−333−30000−i3i3i3−i3
χ7144-4-4-4-4444i−4i−4i4i-21-212-12-12-12-1-21-21−2ii2i−i2i−i−2ii000000000000000000000000000000003−3−330000i3−i3−i3i30000
χ7244-4-4-4-4444i−4i−4i4i-21-212-12-12-12-1-21-21−2ii2i−i2i−i−2ii00000000000000000000000000000000−333−30000−i3i3i3−i30000
χ7344-4-4-4-444−4i4i4i−4i1-21-2-12-12-12-121-21-2−i2ii−2ii−2i−i2i0000000000000000000000000000000000003−3−330000−i3i3i3−i3
χ7444-4-4-4-444−4i4i4i−4i1-21-2-12-12-12-121-21-2−i2ii−2ii−2i−i2i000000000000000000000000000000000000−333−30000i3−i3−i3i3
χ7544-4-4-4-444−4i4i4i−4i-21-212-12-12-12-1-21-212i−i−2ii−2ii2i−i000000000000000000000000000000003−3−330000−i3i3i3−i30000
χ7644-4-4-4-444−4i4i4i−4i-21-212-12-12-12-1-21-212i−i−2ii−2ii2i−i00000000000000000000000000000000−333−30000i3−i3−i3i30000
χ778-88-88i−8i8i−8i00002-4-242-4-242i−4i−2i4i2i−4i−2i4i00000000000000000000000000000000000000000000000000000000
χ788-88-88i−8i8i−8i0000-424-2-424-2−4i2i4i−2i−4i2i4i−2i00000000000000000000000000000000000000000000000000000000
χ798-88-8−8i8i−8i8i00002-4-242-4-24−2i4i2i−4i−2i4i2i−4i00000000000000000000000000000000000000000000000000000000
χ808-88-8−8i8i−8i8i0000-424-2-424-24i−2i−4i2i4i−2i−4i2i00000000000000000000000000000000000000000000000000000000
χ818-8-888i−8i−8i8i00002-4-24-242-42i−4i−2i4i−2i4i2i−4i00000000000000000000000000000000000000000000000000000000
χ828-8-888i−8i−8i8i0000-424-24-2-42−4i2i4i−2i4i−2i−4i2i00000000000000000000000000000000000000000000000000000000
χ838-8-88−8i8i8i−8i00002-4-24-242-4−2i4i2i−4i2i−4i−2i4i00000000000000000000000000000000000000000000000000000000
χ848-8-88−8i8i8i−8i0000-424-24-2-424i−2i−4i2i−4i2i4i−2i00000000000000000000000000000000000000000000000000000000

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