Finite Group DatabasebetaFinite Group Databasebeta| order | 31310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C101 · Schur multiplier (H2) = C1 |
| direct product | C101×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C101) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C101) |
| Fitting, socle, Hall | C31×C101 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C101 |
| Hall | C101×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D31×C101 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C101 |
| Hall | D31 ⋊ C5×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C101 |
| Frattini | C1 | G |
| Fitting, socle | C31×C101 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C101 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3131 |
1313 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31310, 22);