Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
524 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)(18,19,23,20)(21,24,22,25)(26,27,32,37)(28,38,29,40)(30,36,31,35)(33,41,34,39);(19,24)(20,25)(21,22)(26,28)(27,33)(29,32)(30,41)(31,39)(34,37)(35,40)(36,38);(18,20,23,19)(21,25,22,24)(26,29,32,28)(27,34,37,33)(30,41,31,39)(35,40,36,38)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3185);