Finite Group DatabasebetaFinite Group Databasebeta| order | 28308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#13062438⋊C3)⋊C7 |
| unambiguous semidirect product | (#13062438⋊C7)⋊C3 |
| Fitting, socle, derived, Sylow | C337 ⋊ C3×C4×C7 |
| Hall | #13062438⋊C7 ⋊ C3 |
| Hall | (C337⋊C3)⋊C7 ⋊ C4 |
| Hall | #13062438⋊C3 ⋊ C7 |
| Hall | C337⋊C7 ⋊ C3×C4 |
| Hall | #13062438 ⋊ C3×C7 |
| Hall | C337⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C337 | C3×C4×C7 |
| prime radical | (D337⋊C3)⋊C7 | C2 |
| cosocle | D337 | C2×C3×C7 |
| LCS | G ▷ C337 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 337 |
Polycyclic presentation:
2,3,7,2,337|a^2=d,e^a=e^148,e^b=e^128,e^c=e^175,e^d=e^33688 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28308, 32);