Finite Group DatabasebetaFinite Group Databasebeta| order | 28028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C7 |
| direct product | C13×C11⋊#5997 |
| unambiguous semidirect product | C11⋊(C13×#5997) |
| Fitting, socle, Hall | C72×C11×C13 ⋊ C4 |
| derived, Hall | C72×C11 ⋊ C4×C13 |
| Hall | C72×C13 ⋊ Dic11 |
| Hall | C11×C13 ⋊ #5997 |
| Sylow | C72 ⋊ C13×Dic11 |
| Sylow | C11 ⋊ C13×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C11⋊#5997 |
| commutator, hypocenter | C72×C11 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11×C13 | C4 |
| prime radical | C11×C13×C7⋊D7 | C2 |
| cosocle | C11×C7⋊D7 | C2×C13 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2002 |
1898 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28028, 44);