Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12618 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1752 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C17×M32 ◁ G | |
382 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)(18,19,21,26,22,27,32,40,23,24,31,35,33,36,45,47)(20,25,29,38,28,39,41,49,30,34,44,46,42,37,43,48);(19,24)(20,28,30,42)(21,31)(25,37,34,39)(27,36)(29,43,44,41)(32,45)(38,49,46,48);(18,20,21,29,22,28,32,41,23,30,31,44,33,42,45,43)(19,25,26,38,27,39,40,49,24,34,35,46,36,37,47,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5606);