Finite Group DatabasebetaFinite Group Databasebeta| order | 29315 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#14555918 |
| Fitting, socle, Hall | C11×C13×C41 ⋊ C5 |
| derived, Hall | C11×C41 ⋊ C5×C13 |
| Hall | C13×C41 ⋊ C11⋊C5 |
| Hall | C11×C13 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C13×C11⋊C5 |
| Sylow | C11 ⋊ C13×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #14555918 |
| commutator, cosocle, hypocenter | C11×C41 | C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C41 | C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5863 |
1235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29315, 6);