Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12757 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1790 |
| commutator | C2×D4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×#41×C17 ◁ G | |
736 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)(18,19,22,26,23,27,36,43)(20,28,31,45,30,44,48,49)(21,32,34,42,33,25,35,40)(24,37,38,29,39,46,41,47);(18,20,23,30)(19,24,27,39)(21,29,33,47)(22,31,36,48)(25,28,32,44)(26,41,43,38)(34,46,35,37)(40,49,42,45);(25,32)(28,44)(40,42)(45,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5745);