Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11180 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #397 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1440 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
820 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)(20,29,33,25)(21,34,37,44)(22,28)(23,38)(24,27)(26,36,43,39)(30,42)(31,45,32,41)(35,40)(46,48)(47,49);(18,20)(19,25)(21,35)(22,32)(23,31)(24,33)(26,42)(27,29)(28,45)(30,36)(34,46)(37,48)(38,41)(39,47)(40,44)(43,49);(18,21)(19,26,27,43)(20,30)(22,36)(23,39)(24,37)(25,40,29,46)(28,34,38,44)(31,35)(32,48)(33,47)(41,49,45,42)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4168);