Finite Group DatabasebetaFinite Group Databasebeta| order | 27636 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×Dic47 |
| unambiguous semidirect product | C47⋊(C3×C4×C72) |
| derived, Sylow | C47 ⋊ C3×C4×C72 |
| Hall | C3×C72×C47 ⋊ C4 |
| Hall | C72×C47 ⋊ C3×C4 |
| Hall | C3×C47 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | D47 |
| commutator, hypocenter | C47 | C3×C4×C72 |
| Frattini | C2 | C3×C72×D47 |
| Fitting, socle, prime radical | C2×C3×C72×C47 | C2 |
| cosocle | C2×C47 | C2×C3×C72 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C2×C3×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27636 |
7350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27636, 68);