Finite Group Databasebeta

← Group #13099904

Character table — Group #13099904

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11112244444444444444448888888888888888101010101010101020202020202020202020202020202020252525255050100100100100100100100100
order124424551010101010102020202020202020551010101010102020202020202020444444442020202020202020202020202020202022442444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1ii−i−i−i−iii
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1−i−iiiii−i−i
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ911-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-111-11-1i−ii−i
χ1011-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-11−ii−ii
χ1111-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1111-1i−i−ii-111-1
χ1211-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i1-1-11
χ1311-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii1-1-11
χ1411-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1−iii−i-111-1
χ1511-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-11-1−ii−ii
χ1611-1-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-11i−ii−i
χ172222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-222220000000000000000000000002222-2-200000000
χ182222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222000000000000000000000000-2-2-2-22200000000
χ1922-2-22-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000000022-2-22-200000000
χ2022-2-22-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2200000000
χ212-22i−2i0022-2-2000000002i2i−2i−2i220000-2-200002i2i−2i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i0000000000
χ222-22i−2i0022-2-2000000002i2i−2i−2i220000-2-200002i2i−2i−2i1+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i0000000000
χ232-22i−2i0022-2-2000000002i2i−2i−2i220000-2-200002i2i−2i−2i−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i0000000000
χ242-22i−2i0022-2-2000000002i2i−2i−2i220000-2-200002i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i0000000000
χ252-2−2i2i0022-2-200000000−2i−2i2i2i220000-2-20000−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i0000000000
χ262-2−2i2i0022-2-200000000−2i−2i2i2i220000-2-20000−2i−2i2i2i1−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i-222i−2i0000000000
χ272-2−2i2i0022-2-200000000−2i−2i2i2i220000-2-20000−2i−2i2i2i−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i0000000000
χ282-2−2i2i0022-2-200000000−2i−2i2i2i220000-2-20000−2i−2i2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i0000000000
χ294444444-14-144-1-144-1-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000444400000000-1-1-1-1-1-1-1-100000000000000
χ304444444-14-144-1-144-1-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-4-4-4000000001111111100000000000000
χ31444444-14-14-1-144-1-144-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-144440000-1-1-1-1-1-1-1-10000000000000000000000
χ32444444-14-14-1-144-1-144-14-14-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-40000111111110000000000000000000000
χ334444-4-44-14-1-4-411-4-4114-14-1-1-11111-1-11111-1-1-1-10000000000000000i5−i5i5−i5i5−i5i5−i500000000000000
χ344444-4-44-14-1-4-411-4-4114-14-1-1-11111-1-11111-1-1-1-10000000000000000−i5i5−i5i5−i5i5−i5i500000000000000
χ354444-4-4-14-1411-4-411-4-4-14-14-1-11111-1-11111-1-1-1-100000000i5−i5i5−i5i5−i5i5−i50000000000000000000000
χ364444-4-4-14-1411-4-411-4-4-14-14-1-11111-1-11111-1-1-1-100000000−i5i5−i5i5−i5i5−i5i50000000000000000000000
χ3744-4-44-44-14-144-1-1-4-411-41-41-1-1-1-1-1-1-1-11111111100000000000000005−55−5−55−5500000000000000
χ3844-4-44-44-14-144-1-1-4-411-41-41-1-1-1-1-1-1-1-1111111110000000000000000−55−555−55−500000000000000
χ3944-4-44-4-14-14-1-14411-4-41-41-4-1-1-1-1-1-1-1-111111111000000005−55−5−55−550000000000000000000000
χ4044-4-44-4-14-14-1-14411-4-41-41-4-1-1-1-1-1-1-1-11111111100000000−55−555−55−50000000000000000000000
χ4144-4-4-444-14-1-4-41144-1-1-41-41-1-11111-1-1-1-1-1-1111100004i4i−4i−4i00000000−i−i−i−iiiii00000000000000
χ4244-4-4-444-14-1-4-41144-1-1-41-41-1-11111-1-1-1-1-1-111110000−4i−4i4i4i00000000iiii−i−i−i−i00000000000000
χ4344-4-4-44-14-1411-4-4-1-1441-41-4-1-11111-1-1-1-1-1-111114i4i−4i−4i0000−i−i−i−iiiii0000000000000000000000
χ4444-4-4-44-14-1411-4-4-1-1441-41-4-1-11111-1-1-1-1-1-11111−4i−4i4i4i0000iiii−i−i−i−i0000000000000000000000
χ454-44i−4i004-1-41005−500i5−i54i−i−4ii-1-155−5−511i5i5−i5−i5−i−iii00002+2i−2−2i2−2i−2+2i00000000−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ1400000000000000
χ464-44i−4i004-1-41005−500i5−i54i−i−4ii-1-155−5−511i5i5−i5−i5−i−iii0000−2−2i2+2i−2+2i2−2i00000000ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ1400000000000000
χ474-44i−4i004-1-4100−5500−i5i54i−i−4ii-1-1−5−55511−i5−i5i5i5−i−iii00002+2i−2−2i2−2i−2+2i00000000−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ1900000000000000
χ484-44i−4i004-1-4100−5500−i5i54i−i−4ii-1-1−5−55511−i5−i5i5i5−i−iii0000−2−2i2+2i−2+2i2−2i00000000ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ1900000000000000
χ494-44i−4i00-141-45−500i5−i500−i4ii−4i-1-15−55−511i5−i5i5−i5−i−iii2+2i−2−2i2−2i−2+2i0000−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ140000000000000000000000
χ504-44i−4i00-141-45−500i5−i500−i4ii−4i-1-15−55−511i5−i5i5−i5−i−iii−2−2i2+2i−2+2i2−2i0000ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ140000000000000000000000
χ514-44i−4i00-141-4−5500−i5i500−i4ii−4i-1-1−55−5511−i5i5−i5i5−i−iii2+2i−2−2i2−2i−2+2i0000−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ190000000000000000000000
χ524-44i−4i00-141-4−5500−i5i500−i4ii−4i-1-1−55−5511−i5i5−i5i5−i−iii−2−2i2+2i−2+2i2−2i0000ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ190000000000000000000000
χ534-4−4i4i004-1-41005−500−i5i5−4ii4i−i-1-155−5−511−i5−i5i5i5ii−i−i00002−2i−2+2i2+2i−2−2i00000000ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ1400000000000000
χ544-4−4i4i004-1-41005−500−i5i5−4ii4i−i-1-155−5−511−i5−i5i5i5ii−i−i0000−2+2i2−2i−2−2i2+2i00000000−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ1400000000000000
χ554-4−4i4i004-1-4100−5500i5−i5−4ii4i−i-1-1−5−55511i5i5−i5−i5ii−i−i00002−2i−2+2i2+2i−2−2i00000000−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ1900000000000000
χ564-4−4i4i004-1-4100−5500i5−i5−4ii4i−i-1-1−5−55511i5i5−i5−i5ii−i−i0000−2+2i2−2i−2−2i2+2i00000000ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ1900000000000000
χ574-4−4i4i00-141-45−500−i5i500i−4i−i4i-1-15−55−511−i5i5−i5i5ii−i−i2−2i−2+2i2+2i−2−2i0000ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ14ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ140000000000000000000000
χ584-4−4i4i00-141-45−500−i5i500i−4i−i4i-1-15−55−511−i5i5−i5i5ii−i−i−2+2i2−2i−2−2i2+2i0000−ζ3+ζ6−ζ7+ζ14ζ2−ζ11+ζ18−ζ19ζ3−ζ6+ζ7−ζ14−ζ2+ζ11−ζ18+ζ19ζ2+ζ11+ζ18+ζ19ζ3+ζ6+ζ7+ζ14−ζ2−ζ11−ζ18−ζ19−ζ3−ζ6−ζ7−ζ140000000000000000000000
χ594-4−4i4i00-141-4−5500i5−i500i−4i−i4i-1-1−55−5511i5−i5i5−i5ii−i−i2−2i−2+2i2+2i−2−2i0000−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ19ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ190000000000000000000000
χ604-4−4i4i00-141-4−5500i5−i500i−4i−i4i-1-1−55−5511i5−i5i5−i5ii−i−i−2+2i2−2i−2−2i2+2i0000ζ2−ζ11+ζ18−ζ19−ζ3+ζ6−ζ7+ζ14−ζ2+ζ11−ζ18+ζ19ζ3−ζ6+ζ7−ζ14ζ3+ζ6+ζ7+ζ14ζ2+ζ11+ζ18+ζ19−ζ3−ζ6−ζ7−ζ14−ζ2−ζ11−ζ18−ζ190000000000000000000000
χ61888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-23-2-233-23-2-233-23-200000000000000000000000000000000000000
χ62888888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23-233-2-23-233-2-23-2300000000000000000000000000000000000000
χ638888-8-8-2-2-2-222222222-2-2-2-23-2-322-33-2-322-33-23-200000000000000000000000000000000000000
χ648888-8-8-2-2-2-222222222-2-2-2-2-232-3-32-232-3-32-23-2300000000000000000000000000000000000000
χ6588-8-88-8-2-2-2-2-2-2-2-2222222223-23-2-233-2-322-3-32-3200000000000000000000000000000000000000
χ6688-8-88-8-2-2-2-2-2-2-2-222222222-23-233-2-232-3-322-32-300000000000000000000000000000000000000
χ6788-8-8-88-2-2-2-22222-2-2-2-222223-2-322-33-23-2-23-32-3200000000000000000000000000000000000000
χ6888-8-8-88-2-2-2-22222-2-2-2-22222-232-3-32-23-233-22-32-300000000000000000000000000000000000000
χ698-88i−8i00-2-22225−2525−252i5−2i52i5−2i5−2i−2i2i2i3-2−5005-32−i500i53i−2i−3i2i00000000000000000000000000000000000000
χ708-88i−8i00-2-22225−25−25252i5−2i5−2i52i5−2i−2i2i2i-2305−502-30i5−i50−2i3i2i−3i00000000000000000000000000000000000000
χ718-88i−8i00-2-222−252525−25−2i52i52i5−2i5−2i−2i2i2i-230−5502-30−i5i50−2i3i2i−3i00000000000000000000000000000000000000
χ728-88i−8i00-2-222−2525−2525−2i52i5−2i52i5−2i−2i2i2i3-2500−5-32i500−i53i−2i−3i2i00000000000000000000000000000000000000
χ738-8−8i8i00-2-22225−2525−25−2i52i5−2i52i52i2i−2i−2i3-2−5005-32i500−i5−3i2i3i−2i00000000000000000000000000000000000000
χ748-8−8i8i00-2-22225−25−2525−2i52i52i5−2i52i2i−2i−2i-2305−502-30−i5i502i−3i−2i3i00000000000000000000000000000000000000
χ758-8−8i8i00-2-222−252525−252i5−2i5−2i52i52i2i−2i−2i-230−5502-30i5−i502i−3i−2i3i00000000000000000000000000000000000000
χ768-8−8i8i00-2-222−2525−25252i5−2i52i5−2i52i2i−2i−2i3-2500−5-32−i500i5−3i2i3i−2i00000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.