Finite Group DatabasebetaFinite Group Databasebeta| order | 28054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C83 · Schur multiplier (H2) = C13 |
| direct product | C83×C13⋊D13 |
| unambiguous semidirect product | C13⋊(D13×C83) |
| Fitting, socle, Hall | C132×C83 ⋊ C2 |
| derived, Sylow | C132 ⋊ C2×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | C13⋊D13 |
| commutator, cosocle, hypocenter | C132 | C2×C83 |
| Frattini | C1 | G |
| Fitting, socle | C132×C83 | C2 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C83 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14027 |
7138 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28054, 9);