Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D11 |
| commutator | C2×C11 | C22×C4 |
| Fitting | C11×C4⋊C4 | C2 |
| socle, cosocle | C22×C11 | C23 |
| prime radical | C2×D44 | C2 |
| hypercenter | C4⋊C4 | D11 |
| hypocenter | C11 | C4×D4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,13,14,15)(17,19);(16,17,18,19);(2,3)(4,5)(6,7)(8,9)(10,11)(17,19)Polycyclic presentation:
2^5,11|b^2=e,c^2=d,b^a=be,f^a=f^10,c^b=ce70 conjugacy classes — view the full character table.
| maximal subgroup of | #10622369, #10622398, #10622399, … |
| maximal normal subgroup of | #10622369, #10622398, #10622399, … |
| maximal quotient of | #10622267, #10622278, #10622279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 88);