Finite Group DatabasebetaFinite Group Databasebeta| order | 2904 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C112 ⋊ C2×C4 |
| Sylow | C112 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ #11757244 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D33⋊D11 |
| commutator, hypocenter | C3×C112 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C112 | C22 |
| prime radical | C2×C3×C11⋊D11 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 132 |
Polycyclic presentation:
2^3,3,11^2|a^2=c,d^a=d^2,e^a=e^10,e^b=e^10,f^a=e^2f,f^b=f^10222 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#11757244, #72247171, #72247187, … |
| maximal normal subgroup of | D3×#11757244, #72247171, #72247187, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f");;
gap> coll := SingleCollector(F, [2, 2, 2, 3, 11, 11]);;
gap> SetPower(coll, 1, F.3);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^10);;
gap> SetConjugate(coll, 5, 2, F.5^10);;
gap> SetConjugate(coll, 6, 1, F.5^2*F.6);;
gap> SetConjugate(coll, 6, 2, F.6^10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);