Finite Group DatabasebetaFinite Group Databasebeta| order | 34124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#14267798 |
| Fitting, socle, Hall | C19×C449 ⋊ C4 |
| derived, Sylow | C449 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #14267798 |
| commutator, hypocenter | C449 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C449 | C4 |
| prime radical | C19×D449 | C2 |
| cosocle | D449 | C2×C19 |
| LCS | G ▷ C449 | |
| UCS | C1 ◁ C19 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8531 |
2204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34124, 6);