Finite Group DatabasebetaFinite Group Databasebeta| order | 34380 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C191 ⋊ C5×C9 |
| Hall | C22⋊C9×C191 ⋊ C5 |
| Hall | C22×C191⋊C5 ⋊ C9 |
| Sylow | C191 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ C9×C191⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C191⋊C5 |
| commutator, hypocenter | C22×C191 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C191 | C3×C5 |
| prime radical | C22×C3×C191⋊C5 | C3 |
| LCS | G ▷ C22×C191 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3438 |
516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34380, 15);