Finite Group DatabasebetaFinite Group Databasebeta| order | 26052 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊(Dic13⋊C3) |
| unambiguous semidirect product | Dic2171⋊C3 |
| derived, Hall | C13×C167 ⋊ C3×C4 |
| Hall | Dic2171 ⋊ C3 |
| Hall | C13⋊C3×C167 ⋊ C4 |
| Sylow | C167 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ Dic167 |
| Sylow | C13 ⋊ C3×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C13⋊C3)⋊D167 |
| commutator, hypocenter | C13×C167 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C167 | C2×C3 |
| prime radical | C2×C13⋊C3×C167 | C2 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8684 |
Polycyclic presentation:
2,3,13,167,2|a^2=e,c^a=c^12,d^a=d^166,c^b=c^31178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26052, 12);