Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3 |
| direct product | C32×C29×#1181 |
| Fitting, socle, Hall | C32×C292 ⋊ C4 |
| derived | C29 ⋊ C32×C4×C29 |
| Sylow | C292 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C29 | #1181 |
| commutator, hypocenter | C29 | C32×C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C292 | C4 |
| prime radical | C32×C29×D29 | C2 |
| cosocle | D29 | C2×C32×C29 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32×C29 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1044 |
2871 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 111);