Finite Group DatabasebetaFinite Group Databasebeta| order | 31044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C199⋊C3)⋊Dic13 |
| derived, Hall | C13×C199 ⋊ C3×C4 |
| Hall | Dic2587 ⋊ C3 |
| Hall | C13×C199⋊C3 ⋊ C4 |
| Hall | C199⋊C3 ⋊ Dic13 |
| Sylow | C199 ⋊ C3×Dic13 |
| Sylow | C13 ⋊ (C199⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C199⋊C3)⋊D13 |
| commutator, hypocenter | C13×C199 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C199 | C2×C3 |
| prime radical | C2×C13×C199⋊C3 | C2 |
| LCS | G ▷ C13×C199 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10348 |
Polycyclic presentation:
2,3,13,199,2|a^2=e,c^a=c^12,d^a=d^198,d^b=d^106906 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31044, 21);