Finite Group DatabasebetaFinite Group Databasebeta| order | 34072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D4259 |
| unambiguous semidirect product | C4259⋊C23 |
| unambiguous semidirect product | (C2×C4259)⋊C22 |
| Fitting, socle | C22×C4259 ⋊ C2 |
| derived, Sylow | C4259 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D4259 |
| commutator, cosocle, hypocenter | C4259 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C4259 | C2 |
| LCS | G ▷ C4259 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17036 |
8524 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34072, 12);