Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#18229 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1232 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,25)(26,27)(28,35)(29,33)(30,38)(31,34)(32,36)(37,40)(39,41);(18,19)(20,22)(21,23)(24,25)(26,28,31,37)(27,32,34,41)(29,36,30,39)(33,40,38,35);(18,20)(19,22)(21,24)(23,25)(26,27)(28,32)(29,38)(30,33)(31,34)(35,36)(37,41)(39,40);(26,29,31,30)(27,33,34,38)(28,36,37,39)(32,40,41,35)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11217);