Finite Group DatabasebetaFinite Group Databasebeta| order | 31148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic599⋊C13 |
| unambiguous semidirect product | (C599⋊C13)⋊C4 |
| derived, Sylow | C599 ⋊ C4×C13 |
| Hall | C599⋊C13 ⋊ C4 |
| Hall | Dic599 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D599⋊C13 |
| commutator, hypocenter | C599 | C4×C13 |
| Fitting, socle, cosocle | C2×C599 | C2×C13 |
| prime radical | C2×C599⋊C13 | C2 |
| LCS | G ▷ C599 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2396 |
Polycyclic presentation:
2,13,599,2|a^2=d,c^a=c^598,c^b=c^21298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31148, 2);