Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×C31×D25 |
| unambiguous semidirect product | C25⋊(C22×C11×C31) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C11×C31) |
| Fitting | C2×C11×C25×C31 ⋊ C2 |
| derived, Sylow | C25 ⋊ C22×C11×C31 |
| Hall | C11×C25×C31 ⋊ C22 |
| Hall | C25×C31 ⋊ C22×C11 |
| Hall | C11×C25 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C31 | D25 |
| commutator, cosocle, hypocenter | C25 | C22×C11×C31 |
| Frattini | C5 | C2×D5×C11×C31 |
| Fitting | C2×C11×C25×C31 | C2 |
| socle | C2×C5×C11×C31 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C11×C31 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17050 |
9548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 78);