Finite Group DatabasebetaFinite Group Databasebeta| order | 37602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C2089⋊C3 |
| unambiguous semidirect product | (C2×C2089)⋊C32 |
| unambiguous semidirect product | (C2×C3×C2089)⋊C3 |
| Fitting, socle | C2×C3×C2089 ⋊ C3 |
| derived, Sylow | C2089 ⋊ C2×C32 |
| Hall | C2×C2089 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C2089⋊C3 |
| commutator, cosocle, hypocenter | C2089 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C2089 | C3 |
| LCS | G ▷ C2089 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12534 |
4194 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37602, 13);