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×#18231 |
| 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 | |
1200 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
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)(28,37)(29,34)(30,35)(31,40)(32,36)(33,38)(39,41);(18,19)(20,22)(21,23)(24,25)(26,28,32,29)(27,33,36,41)(30,38,31,39)(34,40,37,35);(18,20)(19,22)(21,24)(23,25)(26,29,32,28)(27,34,36,37)(30,38,31,39)(33,40,41,35);(26,30,32,31)(27,35,36,40)(28,38,29,39)(33,34,41,37)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11219);