Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C132 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C3×C132×D17 |
| unambiguous semidirect product | C17⋊(C22×C3×C132) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C3×C132) |
| Fitting, socle | C2×C3×C132×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C22×C3×C132 |
| Hall | C3×C132×C17 ⋊ C22 |
| Hall | C132×C17 ⋊ C22×C3 |
| Hall | C3×C17 ⋊ C22×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C132 | D17 |
| commutator, cosocle, hypocenter | C17 | C22×C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C132×C17 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C3×C132 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17238 |
10140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 262);