Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13460 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2058 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | C2×SD16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,30,44)(21,33)(22,37)(23,26)(24,31,29,45)(25,35)(27,39)(32,46,38,41)(34,40,48,43)(36,47)(42,49);(18,19)(20,29,30,24)(21,25)(22,27)(23,26)(28,31,44,45)(32,43,38,40)(33,35)(34,46,48,41)(36,42)(37,39)(47,49);(18,20,22,38,23,30,39,32)(19,24,27,43,26,29,37,40)(21,34,35,31,36,48,49,45)(25,41,33,28,42,46,47,44)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6448);