Finite Group DatabasebetaFinite Group Databasebeta| order | 32277 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C53 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C3×C29×C53 ⋊ C7 |
| derived, Sylow | C29 ⋊ C3×C7×C53 |
| Hall | C29×C53 ⋊ C3×C7 |
| Hall | C3×C29 ⋊ C7×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C53 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C3×C7×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C53 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C3×C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4611 |
1749 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32277, 2);