Finite Group DatabasebetaFinite Group Databasebeta| order | 28308 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C22×(C337⋊C3)⋊C7 |
| unambiguous semidirect product | (C22×C337⋊C3)⋊C7 |
| Fitting, socle, Hall | C22×C337 ⋊ C3×C7 |
| derived, Sylow | C337 ⋊ C22×C3×C7 |
| Hall | C22×C337⋊C7 ⋊ C3 |
| Hall | C22×C337⋊C3 ⋊ C7 |
| Hall | C337⋊C7 ⋊ C22×C3 |
| Hall | C337⋊C3 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | (C337⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C337 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C337 | C3×C7 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C22 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1348 |
148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28308, 39);