Finite Group DatabasebetaFinite Group Databasebeta| order | 31388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×Dic133 |
| unambiguous semidirect product | C7⋊(C59×Dic19) |
| unambiguous semidirect product | C19⋊(Dic7×C59) |
| derived, Hall | C7×C19 ⋊ C4×C59 |
| Hall | C7×C19×C59 ⋊ C4 |
| Hall | C19×C59 ⋊ Dic7 |
| Hall | C7×C59 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic7×C59 |
| Sylow | C7 ⋊ C59×Dic19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D133 |
| commutator, hypocenter | C7×C19 | C4×C59 |
| Frattini | C2 | C59×D133 |
| Fitting, socle, prime radical | C2×C7×C19×C59 | C2 |
| cosocle | C2×C7×C19 | C2×C59 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C2×C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31388 |
8024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31388, 7);