Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C52⋊C3×D41 |
| unambiguous semidirect product | C41⋊(C2×C3×C52⋊C3) |
| unambiguous semidirect product | (C52×D41)⋊C32 |
| unambiguous semidirect product | (C3×C52×D41)⋊C3 |
| Fitting, socle | C3×C52×C41 ⋊ C2×C3 |
| derived, Hall | C52×C41 ⋊ C2×C32 |
| Hall | C3×C41×C52⋊C3 ⋊ C2 |
| Hall | C52×D41 ⋊ C32 |
| Sylow | C41 ⋊ C2×C3×C52⋊C3 |
| Sylow | C52 ⋊ C32×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C52⋊C3×D41 |
| commutator, cosocle, hypocenter | C52×C41 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1845 |
726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52⋊C3×#4223, C3×#27134237, C3×D41×#3874, … |
| maximal normal subgroup of | C3×C52⋊C3×#4223, C3×#27134237, C3×D41×#3874, … |
| maximal quotient of | C3×C52⋊C3×Dic41, C2×C3×C52⋊C3×D41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 73);