Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
594 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)(19,23)(20,24)(21,25)(26,27)(28,31)(29,32)(30,33)(34,37)(35,38)(36,40)(39,41);(18,19)(20,22)(21,24)(23,25)(26,28,30,35)(27,31,33,38)(29,34,36,41)(32,39,40,37);(18,20,22,19)(21,23,25,24)(26,29)(27,32)(28,34)(30,36)(31,37)(33,40)(35,41)(38,39)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2941);