Finite Group DatabasebetaFinite Group Databasebeta| order | 31188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊D113 |
| unambiguous semidirect product | D339⋊D23 |
| unambiguous semidirect product | D2599⋊D3 |
| Fitting, socle, derived, Hall | C3×C23×C113 ⋊ C22 |
| Hall | C23×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D23 |
| Sylow | C113 ⋊ D3×D23 |
| Hall | C3×C23 ⋊ C2×D113 |
| Sylow | C23 ⋊ D3×D113 |
| Sylow | C3 ⋊ D23×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C113 | C22 |
| LCS | G ▷ C3×C23×C113 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7797 |
Polycyclic presentation:
2^2,3,23,113|d^a=d^22,e^a=e^112,c^b=c^2,d^b=d^222055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31188, 20);