Finite Group DatabasebetaFinite Group Databasebeta| order | 27542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C293 · Schur multiplier (H2) = C1 |
| direct product | D47×C293 |
| unambiguous semidirect product | C47⋊(C2×C293) |
| Fitting, socle, Hall | C47×C293 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C293 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C293 | D47 |
| commutator, cosocle, hypocenter | C47 | C2×C293 |
| Frattini | C1 | G |
| Fitting, socle | C47×C293 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C293 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13771 |
7325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27542, 1);