Finite Group DatabasebetaFinite Group Databasebeta| order | 14895 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C331 ⋊ C3×C5 |
| derived, Sylow | C331 ⋊ C32×C5 |
| Hall | C3×C331⋊C3 ⋊ C5 |
| Hall | C331⋊C5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C331⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C331 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C331 | C3×C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 993 |
111 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(D331⋊C3)⋊C5, C3⋊((D331⋊C3)⋊C5), D3×(C331⋊C3)⋊C5, … |
| maximal normal subgroup of | C3×(D331⋊C3)⋊C5, C3⋊((D331⋊C3)⋊C5), D3×(C331⋊C3)⋊C5, … |
| maximal quotient of | C2×C3×(C331⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14895, 6);