Finite Group DatabasebetaFinite Group Databasebeta| order | 28308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×#13062438⋊C7 |
| unambiguous semidirect product | (C3×#13062438)⋊C7 |
| Fitting, socle, Hall | C3×C337 ⋊ C4×C7 |
| derived, Sylow | C337 ⋊ C3×C4×C7 |
| Hall | C3×C337⋊C7 ⋊ C4 |
| Hall | C3×#13062438 ⋊ C7 |
| Hall | C337⋊C7 ⋊ C3×C4 |
| Hall | #13062438 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13062438⋊C7 |
| commutator, hypocenter | C337 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C337 | C4×C7 |
| prime radical | C3×D337⋊C7 | C2 |
| cosocle | D337 | C2×C3×C7 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1011 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28308, 34);