Finite Group DatabasebetaFinite Group Databasebeta| order | 31155 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×(C31⋊C3)⋊C5 |
| unambiguous semidirect product | (C31⋊C3)⋊(C5×C67) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C3×C67) |
| unambiguous semidirect product | (C67×C31⋊C3)⋊C5 |
| Fitting, socle, Hall | C31×C67 ⋊ C3×C5 |
| derived, Sylow | C31 ⋊ C3×C5×C67 |
| Hall | C67×ΓL(1,𝔽32) ⋊ C3 |
| Hall | C67×C31⋊C3 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C3×C67 |
| Hall | C31⋊C3 ⋊ C5×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | (C31⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C31 | C3×C5×C67 |
| Frattini | C1 | G |
| Fitting, socle | C31×C67 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2077 |
1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31155, 8);