Finite Group DatabasebetaFinite Group Databasebeta| order | 34364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | C2×C11⋊D781 |
| unambiguous semidirect product | (C2×C11)⋊D781 |
| unambiguous semidirect product | (C2×C71)⋊(C11⋊D11) |
| Fitting, socle | C2×C112×C71 ⋊ C2 |
| derived, Hall | C112×C71 ⋊ C22 |
| Sylow | C112 ⋊ C2×D71 |
| Sylow | C71 ⋊ C2×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊D781 |
| commutator, cosocle, hypocenter | C112×C71 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C71 | C2 |
| LCS | G ▷ C112×C71 | |
| UCS | C1 ◁ C2 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17182 |
8594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34364, 28);