Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#23512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C17×#117 ◁ G | |
1414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,21)(23,24)(26,27,31,35)(28,37,38,29)(30,36,32,34)(33,40,39,41);(22,23)(24,25)(26,28)(27,29)(30,33)(31,38)(32,39)(34,40)(35,37)(36,41);(19,21)(22,24,25,23)(26,29,31,37)(27,33,35,39)(28,34,38,36)(30,40,32,41);(26,30,31,32)(27,34,35,36)(28,33,38,39)(29,40,37,41)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16500);