Finite Group DatabasebetaFinite Group Databasebeta| order | 4394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Sylow | 13−1+2 ⋊ C2 |
| derived | C169 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C169 | C2×C13 |
| Frattini, socle | C13 | C13×D13 |
| Fitting | 13−1+2 | C2 |
| LCS | G ▷ C169 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 169 |
Polycyclic presentation:
2,13^3|c^13=d,c^a=c^12d^12,c^b=cd^12,d^a=d^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #72244718, #72244720 |
| maximal normal subgroup of | #72244718, #72244720 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d");;
gap> coll := SingleCollector(F, [2, 13, 13, 13]);;
gap> SetPower(coll, 3, F.4);;
gap> SetConjugate(coll, 3, 1, F.3^12*F.4^12);;
gap> SetConjugate(coll, 3, 2, F.3*F.4^12);;
gap> SetConjugate(coll, 4, 1, F.4^12);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);