Finite Group DatabasebetaFinite Group Databasebeta| order | 28308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#13062438⋊C7) |
| unambiguous semidirect product | (C3⋊#13062438)⋊C7 |
| Fitting, socle, derived, Hall | C3×C337 ⋊ C4×C7 |
| Hall | C3×C337⋊C7 ⋊ C4 |
| Hall | C3⋊#13062438 ⋊ C7 |
| Hall | C337⋊C7 ⋊ Dic3 |
| Sylow | C337 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ #13062438⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C337 | C4×C7 |
| prime radical | C3×D337⋊C7 | C2 |
| cosocle | C3×D337 | C2×C7 |
| LCS | G ▷ C3×C337 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1011 |
Polycyclic presentation:
2,7,2,3,337|a^2=c,d^a=d^2,e^a=e^148,e^b=e^175,e^c=e^33678 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28308, 35);