Finite Group DatabasebetaFinite Group Databasebeta| order | 28548 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #28384434⋊C2 |
| unambiguous semidirect product | #28384438⋊C2 |
| unambiguous semidirect product | #28384442⋊C2 |
| derived, Hall | C13×C61 ⋊ C22×C9 |
| Hall | #20297358 ⋊ C22 |
| Hall | D13×D61 ⋊ C9 |
| Sylow | C61 ⋊ C2×D13⋊C9 |
| Sylow | C13 ⋊ C2×D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #18011723⋊C2 |
| commutator, hypocenter | C13×C61 | C22×C9 |
| Fitting, socle, cosocle | C3×C13×C61 | C22×C3 |
| prime radical | C3×D13×D61 | C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7137 |
Polycyclic presentation:
2^2,3,13,61,3|c^3=f,e^a=e^60,d^b=d^12,d^c=d^3,e^c=e^47288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28548, 42);