Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#13303 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×Q8 | C23×C17 |
| prime radical | C23×C17 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×Q8×C17 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,22)(23,25)(26,27,31,35,32,36,29,33)(28,37,39,30,34,38,41,40);(19,22)(23,24)(26,28,38,35,32,34,37,33)(27,31,41,30,36,29,39,40);(18,20,21,25)(19,23,22,24)(26,29,32,31)(27,33,36,35)(28,39,34,41)(30,38,40,37)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6291);