Finite Group DatabasebetaFinite Group Databasebeta| order | 37716 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×#14267798 |
| unambiguous semidirect product | (C7×#14267798)⋊C3 |
| Fitting, socle, derived, Hall | C7×C449 ⋊ C3×C4 |
| Hall | C7×#14267798 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C449 ⋊ C4 |
| Sylow | C449 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×#14267798 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C449 | C3×C4 |
| prime radical | ΓL(1,𝔽8)×D449 | C2 |
| cosocle | C7×D449 | C2×C3 |
| LCS | G ▷ C7×C449 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3143 |
580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37716, 27);