Finite Group DatabasebetaFinite Group Databasebeta| order | 32214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×ΓL(1,𝔽8)×D59 |
| unambiguous semidirect product | C59⋊(C2×C13×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D59)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | ΓL(1,𝔽8)×D59 |
| commutator, cosocle, hypocenter | C7×C59 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C59 | C2×C3 |
| LCS | G ▷ C7×C59 | |
| UCS | C1 ◁ C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5369 |
2015 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32214, 22);