Finite Group Databasebeta

← Group #13088435

Character table — Group #13088435

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122224444555555666666888810101010101010101010101016161820202020202024242424242430303030303030303030303030303030303072909090
order12336635610448888441212121215153030121212122424242424242424153041212242424242020606060602266668888242424242424242420288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-111-1-1111111111111111111-11111111-111-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111-11-1-111111111111111111111-1111111-11-1-111-11-1-111-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-111-111-1-1-1-11-111-1-11-111-1-1-1-111-1-1-1-11111-1-111
χ7111111111111-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-111-111-1-1-1-1-11-1-111-11-1-11111-1-11111-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111-1-1ii−i−i1111111111-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i111111-1-1-1-1-1-1i−ii−iii−i−iii−i−i1-1i−i
χ101111111111-1-1ii−i−i1-111-1-11111-1-1-1-1iiii−i−i−i−i11-1-1-1ii−i−i1-111-1-1-11-1-111i−i−iiii−i−i−i−iii-11−ii
χ111111111111-1-1ii−i−i-11-1-1111111-1-1-1-1iiii−i−i−i−i11-1-1-1ii−i−i-11-1-1111-111-1-1−iii−i−i−iiiii−i−i-11−ii
χ121111111111-1-1ii−i−i-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i-1-1-1-1-1-1111111−ii−ii−i−iii−i−iii1-1i−i
χ131111111111-1-1−i−iii1111111111-1-1-1-1−i−i−i−iiiii111-1-1−i−iii111111-1-1-1-1-1-1−ii−ii−i−iii−i−iii1-1−ii
χ141111111111-1-1−i−iii1-111-1-11111-1-1-1-1−i−i−i−iiiii11-1-1-1−i−iii1-111-1-1-11-1-111−iii−i−i−iiiii−i−i-11i−i
χ151111111111-1-1−i−iii-11-1-1111111-1-1-1-1−i−i−i−iiiii11-1-1-1−i−iii-11-1-1111-111-1-1i−i−iiii−i−i−i−iii-11i−i
χ161111111111-1-1−i−iii-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii111-1-1−i−iii-1-1-1-1-1-1111111i−ii−iii−i−iii−i−i1-1−ii
χ17222-12-1-12-122222220200-1-12-12-122-1-122-1-122-1-1-1-10-1-1-1-1-1-10200-1-10200-1-100220000-1-1-1-10000
χ18222-12-1-12-122222220-200112-12-122-1-122-1-122-1-1-1-10-1-1-1-1-1-10-200110-2001100-2-2000011110000
χ19222-12-1-12-1222-2-2-2-20200-1-12-12-122-1-1-2-211-2-211-1-10-1-111110200-1-10200-1-100-2-2000011110000
χ20222-12-1-12-1222-2-2-2-20-200112-12-122-1-1-2-211-2-211-1-10-1-111110-200110-2001100220000-1-1-1-10000
χ21222-12-1-12-12-2-22i2i−2i−2i0200-1-12-12-1-2-2112i2i−i−i−2i−2iii-1-1011−i−iii0200-1-10-20011002i−2i0000−i−iii0000
χ22222-12-1-12-12-2-22i2i−2i−2i0-200112-12-1-2-2112i2i−i−i−2i−2iii-1-1011−i−iii0-200110200-1-100−2i2i0000ii−i−i0000
χ23222-12-1-12-12-2-2−2i−2i2i2i0200-1-12-12-1-2-211−2i−2iii2i2i−i−i-1-1011ii−i−i0200-1-10-2001100−2i2i0000ii−i−i0000
χ24222-12-1-12-12-2-2−2i−2i2i2i0-200112-12-1-2-211−2i−2iii2i2i−i−i-1-1011ii−i−i0-200110200-1-1002i−2i0000−i−iii0000
χ2522-12-12-12-1222222220-1-100-12-12-1-122-1-122-1-122-1-10-1-1-1-1-1-120-1-10020-1-1002200-1-1-1-100000000
χ2622-12-12-12-12222222-201100-12-12-1-122-1-122-1-122-1-10-1-1-1-1-1-1-201100-201100-2-200111100000000
χ2722-12-12-12-1222-2-2-2-220-1-100-12-12-1-12211-2-211-2-2-1-10-1-1111120-1-10020-1-100-2-200111100000000
χ2822-12-12-12-1222-2-2-2-2-201100-12-12-1-12211-2-211-2-2-1-10-1-11111-201100-2011002200-1-1-1-100000000
χ2922-12-12-12-12-2-22i2i−2i−2i20-1-100-12-1211-2-2−i−i2i2iii−2i−2i-1-1011−i−iii20-1-100-2011002i−2i00−i−iii00000000
χ3022-12-12-12-12-2-22i2i−2i−2i-201100-12-1211-2-2−i−i2i2iii−2i−2i-1-1011−i−iii-20110020-1-100−2i2i00ii−i−i00000000
χ3122-12-12-12-12-2-2−2i−2i2i2i20-1-100-12-1211-2-2ii−2i−2i−i−i2i2i-1-1011ii−i−i20-1-100-201100−2i2i00ii−i−i00000000
χ3222-12-12-12-12-2-2−2i−2i2i2i-201100-12-1211-2-2ii−2i−2i−i−i2i2i-1-1011ii−i−i-20110020-1-1002i−2i00−i−iii00000000
χ332-222-2-222-2-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000022-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132-202i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ342-222-2-222-2-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000022-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132-202i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ352-222-2-222-2-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000022-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232-20−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ362-222-2-222-2-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000022-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232-20−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ372-22-1-21-121-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300003−32-1-212i−2i−ii2ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ13-110−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300003−30000−i3i300000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ382-22-1-21-121-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−332-1-212i−2i−ii2ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ13-110−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000−330000i3−i300000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ392-22-1-21-121-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300003−32-1-212i−2i−ii−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13-110−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300003−30000−i3i300000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ402-22-1-21-121-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−332-1-212i−2i−ii−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13-110−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000−330000i3−i300000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ412-22-1-21-121-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300003−32-1-21−2i2ii−i−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23-110i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300003−30000i3−i300000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ422-22-1-21-121-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−332-1-21−2i2ii−i−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23-110i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000−330000−i3i300000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ432-22-1-21-121-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300003−32-1-21−2i2ii−i2ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ23-110i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300003−30000i3−i300000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ442-22-1-21-121-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−332-1-21−2i2ii−i2ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ23-110i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000−330000−i3i300000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ452-2-121-2-121-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13003−300-121-2−ii2i−2i−ζ7−ζ23ζ7+ζ232ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13−ζ5−ζ13−2ζ5−2ζ132ζ5+2ζ13-110−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13003−30000−i3i3000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ462-2-121-2-121-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−3300-121-2−ii2i−2i−ζ7−ζ23ζ7+ζ232ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13−ζ5−ζ13−2ζ5−2ζ132ζ5+2ζ13-110−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1300−330000i3−i3000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ472-2-121-2-121-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13003−300-121-2−ii2i−2iζ7+ζ23−ζ7−ζ23−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13ζ5+ζ132ζ5+2ζ13−2ζ5−2ζ13-110−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13003−30000−i3i3000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ482-2-121-2-121-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−3300-121-2−ii2i−2iζ7+ζ23−ζ7−ζ23−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13ζ5+ζ132ζ5+2ζ13−2ζ5−2ζ13-110−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1300−330000i3−i3000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ492-2-121-2-121-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23003−300-121-2i−i−2i2iζ5+ζ13−ζ5−ζ13−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23ζ7+ζ232ζ7+2ζ23−2ζ7−2ζ23-110i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23003−30000i3−i3000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ502-2-121-2-121-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−3300-121-2i−i−2i2iζ5+ζ13−ζ5−ζ13−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23ζ7+ζ232ζ7+2ζ23−2ζ7−2ζ23-110i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2300−330000−i3i3000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ512-2-121-2-121-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23003−300-121-2i−i−2i2i−ζ5−ζ13ζ5+ζ132ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23−ζ7−ζ23−2ζ7−2ζ232ζ7+2ζ23-110i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23003−30000i3−i3000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ522-2-121-2-121-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−3300-121-2i−i−2i2i−ζ5−ζ13ζ5+ζ132ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23−ζ7−ζ23−2ζ7−2ζ232ζ7+2ζ23-110i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2300−330000−i3i3000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ534444444-14-1000000444444-1-1-1-1000000000000-1-14000000-1-1-1-1-1-1000000000000000000-1000
χ544444444-14-10000004-444-4-4-1-1-1-1000000000000-1-1-4000000-11-1-1110000000000000000001000
χ554444444-14-1000000-44-4-444-1-1-1-1000000000000-1-1-40000001-111-1-10000000000000000001000
χ564444444-14-1000000-4-4-4-4-4-4-1-1-1-1000000000000-1-14000000111111000000000000000000-1000
χ5744-2-2-2-21414444444000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21101111110000000000000000000000000000
χ5844-2-2-2-2141444-4-4-4-4000000-2-2-2-2-2-2-2-22222222211011-1-1-1-10000000000000000000000000000
χ5944-2-2-2-21414-4-44i4i−4i−4i000000-2-2-2-22222−2i−2i−2i−2i2i2i2i2i110-1-1ii−i−i0000000000000000000000000000
χ6044-2-2-2-21414-4-4−4i−4i4i4i000000-2-2-2-222222i2i2i2i−2i−2i−2i−2i110-1-1−i−iii0000000000000000000000000000
χ614-4-2-22214-1-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000-2-222−2i2i−2i2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ131-10i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000000000000000000000
χ624-4-2-22214-1-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000-2-222−2i2i−2i2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ131-10i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000000000000000000000
χ634-4-2-22214-1-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23000000-2-2222i−2i2i−2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ231-10−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000000000000000000000
χ644-4-2-22214-1-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000-2-2222i−2i2i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ231-10−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000000000000000000000
χ65888-48-4-4-2-4-20000000800-4-4-21-210000000000001100000000-200110000000000000000000000
χ66888-48-4-4-2-4-20000000-80044-21-210000000000001100000000200-1-10000000000000000000000
χ6788-48-48-4-2-4-200000080-4-4001-21-2000000000000110000000-2011000000000000000000000000
χ6888-48-48-4-2-4-2000000-8044001-21-200000000000011000000020-1-1000000000000000000000000
χ698-888-8-88-2-82000000000000-2-222000000000000-2200000000000000000000000000000000000
χ708-88-4-84-4-242000000000043−43-212-10000000000001-100000000000−330000000000000000000000
χ718-88-4-84-4-2420000000000−4343-212-10000000000001-1000000000003−30000000000000000000000
χ728-8-484-8-4-2420000000043−43001-2-120000000000001-1000000000−33000000000000000000000000
χ738-8-484-8-4-24200000000−4343001-2-120000000000001-10000000003−3000000000000000000000000
χ741616-8-8-8-84-44-40000000000002222000000000000-1-100000000000000000000000000000000000
χ7516-16-8-8884-4-4400000000000022-2-2000000000000-1100000000000000000000000000000000000

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