Finite Group DatabasebetaFinite Group Databasebeta| order | 27636 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C47 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×ΓL(1,𝔽8)×C47 |
| Fitting, socle | C2×C72×C47 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C47 |
| Hall | C2×C7×D7×C47 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8)×C47 ⋊ C22 |
| Hall | C72×C47 ⋊ C22×C3 |
| Hall | C2×C7×D7 ⋊ C3×C47 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C22×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D7×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C72 | C22×C3×C47 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C47 | C2×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C47 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3948 |
2350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27636, 102);