Finite Group DatabasebetaFinite Group Databasebeta| order | 28028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×Dic143 |
| unambiguous semidirect product | C11⋊(C49×Dic13) |
| derived, Hall | C11×C13 ⋊ C4×C49 |
| Hall | C11×C13×C49 ⋊ C4 |
| Hall | C13×C49 ⋊ Dic11 |
| Hall | C11×C49 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic11×C49 |
| Sylow | C11 ⋊ C49×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D143 |
| commutator, hypocenter | C11×C13 | C4×C49 |
| Frattini | C2×C7 | C7×D143 |
| Fitting | C2×C11×C13×C49 | C2 |
| socle, prime radical, cosocle | C2×C7×C11×C13 | C2×C7 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C2×C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28028 |
7154 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28028, 4);