Finite Group DatabasebetaFinite Group Databasebeta| order | 28197 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×C241⋊C3 |
| unambiguous semidirect product | C241⋊(C32×C13) |
| unambiguous semidirect product | (C3×C241)⋊(C3×C13) |
| Fitting, socle | C3×C13×C241 ⋊ C3 |
| derived, Sylow | C241 ⋊ C32×C13 |
| Hall | C13×C241 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C241⋊C3 |
| commutator, cosocle, hypocenter | C241 | C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C241 | C3 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C3×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9399 |
3237 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28197, 8);