Finite Group DatabasebetaFinite Group Databasebeta| order | 34132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D1219 |
| unambiguous semidirect product | (C2×C23)⋊(C7×D53) |
| unambiguous semidirect product | (C2×C53)⋊(C7×D23) |
| Fitting, socle | C2×C7×C23×C53 ⋊ C2 |
| derived, Hall | C23×C53 ⋊ C22×C7 |
| Hall | C7×C23×C53 ⋊ C22 |
| Hall | C7×C53 ⋊ C2×D23 |
| Hall | C7×C23 ⋊ C2×D53 |
| Sylow | C53 ⋊ C2×C7×D23 |
| Sylow | C23 ⋊ C2×C7×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D1219 |
| commutator, cosocle, hypocenter | C23×C53 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C23×C53 | C2 |
| LCS | G ▷ C23×C53 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17066 |
8554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34132, 23);