Finite Group DatabasebetaFinite Group Databasebeta| order | 31710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×ΓL(1,𝔽8)×D151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | ΓL(1,𝔽8)×D151 |
| commutator, cosocle, hypocenter | C7×C151 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C151 | C2×C3 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5285 |
1925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31710, 34);