Finite Group DatabasebetaFinite Group Databasebeta| order | 26052 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2171 |
| unambiguous semidirect product | C167⋊(C3×Dic13) |
| derived, Hall | C13×C167 ⋊ C3×C4 |
| Hall | C3×C13×C167 ⋊ C4 |
| Hall | C3×C167 ⋊ Dic13 |
| Sylow | C167 ⋊ C3×Dic13 |
| Hall | C3×C13 ⋊ Dic167 |
| Sylow | C13 ⋊ C3×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2171 |
| commutator, hypocenter | C13×C167 | C3×C4 |
| Frattini | C2 | C3×D2171 |
| Fitting, socle, prime radical | C2×C3×C13×C167 | C2 |
| cosocle | C2×C13×C167 | C2×C3 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26052 |
6522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26052, 5);