Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#11691 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #99 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C17 |
| socle | C22×C17 | C2×#99 |
| prime radical | C17×#392 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C4×C17 ◁ C2×C17×#117 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(20,22)(21,24)(23,25)(26,27)(28,32)(29,36,37,31)(30,33)(34,40,41,38)(35,39);(19,22)(20,25)(23,24)(27,31)(32,38)(33,36)(39,40);(26,28,30,35)(27,32,33,39)(29,34,37,41)(31,38,36,40)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4679);