Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D11 |
| commutator | C2×C11 | C42 |
| Fitting | C42×C11 | C2 |
| socle, prime radical | C22×C11 | C2×C4 |
| cosocle | C2×C4×C11 | C22 |
| hypercenter | C42 | D11 |
| hypocenter | C11 | #97 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,13,14,15)(17,20)(21,23);(2,3)(4,5)(6,7)(8,9)(10,11)(16,17,18,21,19,20,22,23)Polycyclic presentation:
2^5,11|a^2=c,b^2=d,c^2=e,b^a=be,f^a=f^10100 conjugacy classes — view the full character table.
| maximal subgroup of | #10622102, #10622103, #10622178, … |
| maximal normal subgroup of | #10622102, #10622103, #10622178, … |
| maximal quotient of | #10622092, #10622104, #10622162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 9);