Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle | C2×C3×C52×C41 ⋊ C3 |
| derived, Sylow | C52 ⋊ C2×C32×C41 |
| Hall | C2×C52×C41 ⋊ C32 |
| Hall | C52×C41 ⋊ C2×C32 |
| Hall | C2×C52 ⋊ C32×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C41 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C32×C41 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C41 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C3×C41 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3690 |
2706 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C41×#64470, C3×#27134196, C3×C41×#1039⋊C3, … |
| maximal normal subgroup of | C3×C41×#64470, C3×#27134196, C3×C41×#1039⋊C3, … |
| maximal quotient of | C3×C4×C41×C52⋊C3, C22×C3×C41×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 81);