Finite Group DatabasebetaFinite Group Databasebeta| order | 8190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#13109900 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊#10587720 |
| commutator, hypocenter | C5×C7×C13 | C2×C9 |
| Fitting, socle | C3×C5×C7×C13 | C2×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,13,3|b^3=f,c^a=c^4,d^a=d^6,d^b=d^2,e^b=e^3279 conjugacy classes — view the full character table.
| maximal subgroup of | #13109896⋊D5, #13109902⋊D5, D5×#13109900, … |
| maximal normal subgroup of | #13109896⋊D5, #13109902⋊D5, D5×#13109900, … |
| maximal quotient of | #30654993, C2×C5⋊#13109900 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8190, 43);