Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C61 · Schur multiplier (H2) = C2×C5 |
| direct product | C61×C22⋊(C52⋊C3) |
| unambiguous semidirect product | C22⋊(C61×C52⋊C3) |
| unambiguous semidirect product | C52⋊(A4×C61) |
| Fitting, socle, Hall | C22×C52×C61 ⋊ C3 |
| derived, Hall | C22×C52 ⋊ C3×C61 |
| Hall | C52×C61 ⋊ A4 |
| Hall | C22×C61 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ A4×C61 |
| Sylow | C22 ⋊ C61×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C22⋊(C52⋊C3) |
| commutator, cosocle, hypocenter | C22×C52 | C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C61 | C3 |
| LCS | G ▷ C22×C52 | |
| UCS | C1 ◁ C61 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1830 |
2196 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 270);