Finite Group DatabasebetaFinite Group Databasebeta| order | 31602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D229⋊C3 |
| unambiguous semidirect product | D229⋊(C3×C23) |
| unambiguous semidirect product | (C229⋊C3)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D229)⋊C3 |
| Fitting, socle, Hall | C23×C229 ⋊ C2×C3 |
| derived, Sylow | C229 ⋊ C2×C3×C23 |
| Hall | C23×C229⋊C3 ⋊ C2 |
| Hall | C23×D229 ⋊ C3 |
| Hall | C229⋊C3 ⋊ C2×C23 |
| Hall | D229 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D229⋊C3 |
| commutator, cosocle, hypocenter | C229 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C229 | C2×C3 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5267 |
1012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31602, 10);