Finite Group Databasebeta

← Group #13018225

Character table — Group #13018225

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111444444444444448888888888888888101010101010101010101010161616161616161620204040404040404040404040404040404040404040
order12222222444444510101010101010224420202020202020202020202044444444444410101010202020204422448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-222-2-2222222220000-2-2-2-22222-2-2-2-222-2-2222222-2-200000000-2-200000000000000000000
χ1822222222-2-222-2-2222222220000-2-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-222000000002200000000000000000000
χ1922222222-2-2-2-222222222220000-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2000000002200000000000000000000
χ2022222222-2-2-2-222222222220000-2-2-2-2-2-2-2-22222-2-2222222-2-22200000000-2-200000000000000000000
χ2122-2-222-2-200002i−2i222-22-2-2-20000000000002i2i−2i−2i002-22i2i−2i−2i002-200000000000000i2−i22−20000i2−i22−20000
χ2222-2-222-2-200002i−2i222-22-2-2-20000000000002i2i−2i−2i002-22i2i−2i−2i002-200000000000000−i2i2−220000−i2i2−220000
χ2322-2-222-2-200002i−2i222-22-2-2-20000000000002i2i−2i−2i00-22−2i−2i2i2i00-22000000000000002−2−i2i20000−22i2−i20000
χ2422-2-222-2-200002i−2i222-22-2-2-20000000000002i2i−2i−2i00-22−2i−2i2i2i00-2200000000000000−22i2−i200002−2−i2i20000
χ2522-2-222-2-20000−2i2i222-22-2-2-2000000000000−2i−2i2i2i002-2−2i−2i2i2i002-200000000000000i2−i2−220000i2−i2−220000
χ2622-2-222-2-20000−2i2i222-22-2-2-2000000000000−2i−2i2i2i002-2−2i−2i2i2i002-200000000000000−i2i22−20000−i2i22−20000
χ2722-2-222-2-20000−2i2i222-22-2-2-2000000000000−2i−2i2i2i00-222i2i−2i−2i00-22000000000000002−2i2−i20000−22−i2i20000
χ2822-2-222-2-20000−2i2i222-22-2-2-2000000000000−2i−2i2i2i00-222i2i−2i−2i00-2200000000000000−22−i2i200002−2i2−i20000
χ292-22-22-22-2002i−2i0022-22-22-2-2000000002i2i−2i−2i00002-2002i−2i2i−2i2-2000000000000000000002−2i2−i200002−2i2−i2
χ302-22-22-22-2002i−2i0022-22-22-2-2000000002i2i−2i−2i00002-2002i−2i2i−2i2-200000000000000000000−22−i2i20000−22−i2i2
χ312-22-22-22-2002i−2i0022-22-22-2-2000000002i2i−2i−2i0000-2200−2i2i−2i2i-2200000000000000000000i2−i2−220000−i2i22−2
χ322-22-22-22-2002i−2i0022-22-22-2-2000000002i2i−2i−2i0000-2200−2i2i−2i2i-2200000000000000000000−i2i22−20000i2−i2−22
χ332-22-22-22-200−2i2i0022-22-22-2-200000000−2i−2i2i2i00002-200−2i2i−2i2i2-2000000000000000000002−2−i2i200002−2−i2i2
χ342-22-22-22-200−2i2i0022-22-22-2-200000000−2i−2i2i2i00002-200−2i2i−2i2i2-200000000000000000000−22i2−i20000−22i2−i2
χ352-22-22-22-200−2i2i0022-22-22-2-200000000−2i−2i2i2i0000-22002i−2i2i−2i-2200000000000000000000i2−i22−20000−i2i2−22
χ362-22-22-22-200−2i2i0022-22-22-2-200000000−2i−2i2i2i0000-22002i−2i2i−2i-2200000000000000000000−i2i2−220000i2−i22−2
χ372-2-22-222-22-200002-222-2-22-2002i−2i22-2-20000000022-2-20000-2-22200002i2i−2i−2i00002i−2i0000000000000000
χ382-2-22-222-22-200002-222-2-22-2002i−2i22-2-200000000-2-222000022-2-200002i2i−2i−2i0000−2i2i0000000000000000
χ392-2-22-222-22-200002-222-2-22-200−2i2i22-2-20000000022-2-20000-2-2220000−2i−2i2i2i0000−2i2i0000000000000000
χ402-2-22-222-22-200002-222-2-22-200−2i2i22-2-200000000-2-222000022-2-20000−2i−2i2i2i00002i−2i0000000000000000
χ412-2-22-222-2-2200002-222-2-22-22-200-2-2220000000022220000-2-2-2-222-2-20000002-2000000000000000000
χ422-2-22-222-2-2200002-222-2-22-22-200-2-22200000000-2-2-2-20000222222-2-2000000-22000000000000000000
χ432-2-22-222-2-2200002-222-2-22-2-2200-2-2220000000022220000-2-2-2-2-2-222000000-22000000000000000000
χ442-2-22-222-2-2200002-222-2-22-2-2200-2-22200000000-2-2-2-200002222-2-2220000002-2000000000000000000
χ4544444444444444-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-10000000000000000000000
χ4644444444444444-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111110000000000000000000000
χ474444444444-4-4-4-4-1-1-1-1-1-1-1-144-4-4-1-1-1-111111111000000000000-1-1-1-111110000000000000000000000
χ484444444444-4-4-4-4-1-1-1-1-1-1-1-1-4-444-1-1-1-1111111110000000000001111-1-1-1-10000000000000000000000
χ4944444444-4-444-4-4-1-1-1-1-1-1-1-100001111-1-1-1-111110000000000005−55−55−55−50000000000000000000000
χ5044444444-4-444-4-4-1-1-1-1-1-1-1-100001111-1-1-1-11111000000000000−55−55−55−550000000000000000000000
χ5144444444-4-4-4-444-1-1-1-1-1-1-1-1000011111111-1-1-1-10000000000005−55−5−55−550000000000000000000000
χ5244444444-4-4-4-444-1-1-1-1-1-1-1-1000011111111-1-1-1-1000000000000−55−555−55−50000000000000000000000
χ534444-4-4-4-40000004-4-4-4444-40000000000000000000000000000000000004i−4i00000000000000000000
χ544444-4-4-4-40000004-4-4-4444-4000000000000000000000000000000000000−4i4i00000000000000000000
χ5544-4-4-4-4440000004-4-444-4-4400000000000000004-4000000-4400000000000000000000000000000000
χ5644-4-4-4-4440000004-4-444-4-440000000000000000-440000004-400000000000000000000000000000000
χ574-44-4-44-440000004-44-4-44-440000000000000000004-4000000-44000000000000000000000000000000
χ584-44-4-44-440000004-44-4-44-44000000000000000000-440000004-4000000000000000000000000000000
χ594-4-444-4-4400000044-4-4-4-444000000000000000000004-4-440000000000000000000000000000000000
χ604-4-444-4-4400000044-4-4-4-44400000000000000000000-444-40000000000000000000000000000000000
χ614-4-44-444-44-40000-11-1-111-11004i−4i-1-111i5−i5i5−i5i5−i5i5−i50000000000005−5−55−i−iii0000000000000000000000
χ624-4-44-444-44-40000-11-1-111-11004i−4i-1-111−i5i5−i5i5−i5i5−i5i5000000000000−555−5−i−iii0000000000000000000000
χ634-4-44-444-44-40000-11-1-111-1100−4i4i-1-111i5−i5i5−i5i5−i5i5−i5000000000000−555−5ii−i−i0000000000000000000000
χ644-4-44-444-44-40000-11-1-111-1100−4i4i-1-111−i5i5−i5i5−i5i5−i5i50000000000005−5−55ii−i−i0000000000000000000000
χ654-4-44-444-4-440000-11-1-111-114-40011-1-1i5−i5i5−i5−i5i5−i5i5000000000000-1-111i5−i5−i5i50000000000000000000000
χ664-4-44-444-4-440000-11-1-111-114-40011-1-1−i5i5−i5i5i5−i5i5−i5000000000000-1-111−i5i5i5−i50000000000000000000000
χ674-4-44-444-4-440000-11-1-111-11-440011-1-1i5−i5i5−i5−i5i5−i5i500000000000011-1-1−i5i5i5−i50000000000000000000000
χ684-4-44-444-4-440000-11-1-111-11-440011-1-1−i5i5−i5i5i5−i5i5−i500000000000011-1-1i5−i5−i5i50000000000000000000000
χ698888-8-8-8-8000000-2222-2-2-22000025−2525−2500000000000000000000000000000000000000000000000000
χ708888-8-8-8-8000000-2222-2-2-220000−2525−252500000000000000000000000000000000000000000000000000
χ7188-8-888-8-800008i−8i-2-2-22-2222000000000000−2i−2i2i2i000000000000000000000000000000000000000000
χ7288-8-888-8-80000−8i8i-2-2-22-22220000000000002i2i−2i−2i000000000000000000000000000000000000000000
χ7388-8-8-8-888000000-222-2-222-20000000025−25−25250000000000000000000000000000000000000000000000
χ7488-8-8-8-888000000-222-2-222-200000000−252525−250000000000000000000000000000000000000000000000
χ758-88-88-88-8008i−8i00-2-22-22-22200000000−2i−2i2i2i0000000000000000000000000000000000000000000000
χ768-88-88-88-800−8i8i00-2-22-22-222000000002i2i−2i−2i0000000000000000000000000000000000000000000000
χ778-88-8-88-88000000-22-222-22-200000000000025−25−2525000000000000000000000000000000000000000000
χ788-88-8-88-88000000-22-222-22-2000000000000−252525−25000000000000000000000000000000000000000000
χ798-8-888-8-88000000-2-22222-2-2000025−25−252500000000000000000000000000000000000000000000000000
χ808-8-888-8-88000000-2-22222-2-20000−252525−2500000000000000000000000000000000000000000000000000

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