Finite Group DatabasebetaFinite Group Databasebeta| order | 34235 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C167 · Schur multiplier (H2) = C1 |
| direct product | C167×C41⋊C5 |
| unambiguous semidirect product | C41⋊(C5×C167) |
| unambiguous semidirect product | (C41×C167)⋊C5 |
| Fitting, socle, Hall | C41×C167 ⋊ C5 |
| derived, Sylow | C41 ⋊ C5×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C5×C167 |
| Frattini | C1 | G |
| Fitting, socle | C41×C167 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6847 |
2171 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34235, 1);