Finite Group DatabasebetaFinite Group Databasebeta| order | 36738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C32×D157⋊C13 |
| unambiguous semidirect product | (C32×D157)⋊C13 |
| Fitting, socle, Hall | C32×C157 ⋊ C2×C13 |
| derived, Sylow | C157 ⋊ C2×C32×C13 |
| Hall | C32×C157⋊C13 ⋊ C2 |
| Hall | C32×D157 ⋊ C13 |
| Hall | C157⋊C13 ⋊ C2×C32 |
| Hall | D157 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D157⋊C13 |
| commutator, cosocle, hypocenter | C157 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C157 | C2×C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1413 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36738, 36);