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) = C26 |
| direct product | C17×#10793 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C4×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | C22⋊#95 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×M16×C17 ◁ G | |
1164 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)(20,25,31,40)(21,33)(22,29)(23,28)(24,27)(26,35)(30,44,46,48)(32,42,36,39)(34,43)(37,41)(38,47,49,45);(18,20,23,32,24,31,22,36)(19,25,29,39,27,40,28,42)(21,30,35,47,34,46,37,45)(26,38,33,48,41,49,43,44);(18,21)(19,26)(20,30)(22,37)(23,35)(24,34)(25,38)(27,41)(28,43)(29,33)(31,46)(32,47)(36,45)(39,48)(40,49)(42,44)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3781);