Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #66890 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #4323 |
| commutator, cosocle | C8×C11 | C22 |
| Frattini | C8 | C2×D11 |
| Fitting | C11×D8 | C2 |
| socle | C2×C11 | D8 |
| hypercenter | D8 | D11 |
| hypocenter | C11 | D16 |
| LCS | G ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,8,10,11,9,7,5,3)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)Polycyclic presentation:
2^5,11|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^10,c^b=cd,d^b=de46 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D16, #10622524, #10622527, … |
| maximal normal subgroup of | D11×D16, #10622524, #10622527, … |
| maximal quotient of | #10622127, #10622129, #10622157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 32);