Finite Group DatabasebetaFinite Group Databasebeta| order | 351 |
| isoclinism | isoclinic class of #66848 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C13 ⋊ 3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×C13⋊C3 |
| commutator, socle, cosocle | C3×C13 | C32 |
| Fitting, prime radical | C32×C13 | C3 |
| hypercenter | C32 | C13⋊C3 |
| hypocenter | C13 | 3−1+2 |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C3 ◁ C32 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 117 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,4,3,6,10,7,11,13,5,8,12,9)(15,18,19)(17,21,22);(2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15,17,16,19,21,20,18,22)Polycyclic presentation:
3^3,13|a^3=c,b^a=bc,d^a=d^347 conjugacy classes — view the full character table.
| maximal subgroup of | #66851⋊C2, C2×#66851, #11760434, … |
| maximal normal subgroup of | #66851⋊C2, C2×#66851, #11760434, … |
| maximal quotient of | C2×#66851, C32⋊(C13⋊C9), (C13⋊C9)⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(351, 7);