Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#99 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C17 |
| prime radical | C17×#2617 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C24×C17 ◁ C22×C22⋊C4×C17 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,22)(21,24)(23,25)(26,27)(28,34)(29,37,38,32)(30,33)(31,36,39,41)(35,40);(19,22)(20,25)(23,24)(26,28)(27,31)(29,36)(30,35)(32,34)(33,39)(37,40)(38,41);(28,35)(31,39)(34,40)(36,41)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4680);