Finite Group DatabasebetaFinite Group Databasebeta| order | 31188 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C23⋊#90673) |
| unambiguous semidirect product | C23⋊(C3⋊#90673) |
| Fitting, socle, derived, Hall | C3×C23×C113 ⋊ C4 |
| Hall | C23×C113 ⋊ Dic3 |
| Hall | C3×C113 ⋊ Dic23 |
| Sylow | C113 ⋊ Dic69 |
| Hall | C3×C23 ⋊ #90673 |
| Sylow | C23 ⋊ C3⋊#90673 |
| Sylow | C3 ⋊ C23⋊#90673 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C23×C113 | C4 |
| prime radical, cosocle | C3×C23×D113 | C2 |
| LCS | G ▷ C3×C23×C113 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7797 |
Polycyclic presentation:
2^2,3,23,113|a^2=b,c^a=c^2,d^a=d^22,e^a=e^15,e^b=e^1122004 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31188, 15);