Finite Group DatabasebetaFinite Group Databasebeta| order | 30972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C29×#67063 |
| Fitting, socle, Hall | C3×C29×C89 ⋊ C4 |
| derived, Sylow | C89 ⋊ C3×C4×C29 |
| Hall | C29×C89 ⋊ C3×C4 |
| Hall | C3×C89 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | #67063 |
| commutator, hypocenter | C89 | C3×C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C89 | C4 |
| prime radical | C3×C29×D89 | C2 |
| cosocle | D89 | C2×C3×C29 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7743 |
2262 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30972, 10);