Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#10013 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #392 |
| prime radical | C17×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
598 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)(19,22)(20,24)(23,25)(26,27)(28,34)(29,37)(30,33)(31,35)(32,39)(36,41)(38,40);(18,19,21,23)(20,25,24,22)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(18,19)(20,25)(21,23)(22,24)(31,40)(34,41)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3001);