Finite Group DatabasebetaFinite Group Databasebeta| order | 29068 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#10621728 |
| Fitting, socle, Hall | C132×C43 ⋊ C4 |
| derived, Sylow | C132 ⋊ C4×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #10621728 |
| commutator, hypocenter | C132 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C132×C43 | C4 |
| prime radical | C43×C13⋊D13 | C2 |
| cosocle | C13⋊D13 | C2×C43 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C43 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7267 |
1978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29068, 30);