Finite Group DatabasebetaFinite Group Databasebeta| order | 34192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#22555459 |
| unambiguous semidirect product | D2137⋊(C2×C4) |
| Fitting, socle | C22×C2137 ⋊ C4 |
| derived, Sylow | C2137 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #22555459 |
| commutator, hypocenter | C2137 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C2137 | C4 |
| prime radical | C22×D2137 | C2 |
| cosocle | D2137 | C23 |
| LCS | G ▷ C2137 | |
| UCS | C1 ◁ C22 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8548 |
2152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34192, 51);