Finite Group DatabasebetaFinite Group Databasebeta| order | 2970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C11×H(3,𝔽3) ⋊ C2×C5 |
| Hall | H(3,𝔽3)×C11⋊C5 ⋊ C2 |
| Hall | C11⋊#272 ⋊ C5 |
| Hall | C11⋊C5 ⋊ #272 |
| Sylow | H(3,𝔽3) ⋊ AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×#272 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C3⋊(C3⋊AGL(1,𝔽11)) |
| commutator, Fitting, cosocle, hypocenter | C11×H(3,𝔽3) | C2×C5 |
| socle | C3×C11 | C5×C3⋊D3 |
| LCS | G ▷ C11×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
Polycyclic presentation:
2,5,3^2,11,3|c^a=c^2,d^a=d^2,d^c=df,e^a=e^10,e^b=e^461 conjugacy classes — view the full character table.
| maximal subgroup of | #72259120, #272×AGL(1,𝔽11) |
| maximal normal subgroup of | #72259120, #272×AGL(1,𝔽11) |
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, 5, 3, 3, 11, 3]);;
gap> SetConjugate(coll, 3, 1, F.3^2);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 4, 3, F.4*F.6);;
gap> SetConjugate(coll, 5, 1, F.5^10);;
gap> SetConjugate(coll, 5, 2, F.5^4);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);