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×#10792 |
| 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 ◁ C2×C17×#117 ◁ G | |
1204 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)(20,24,29,40)(21,31)(22,34)(23,26)(25,33)(27,37)(28,44,46,48)(30,42,35,39)(32,43)(36,41)(38,47,49,45);(18,20)(19,24,26,40)(21,28)(22,35)(23,29)(25,38,41,49)(27,42,34,39)(30,37)(31,48,43,44)(32,46)(33,47)(36,45);(18,21)(19,25)(20,28)(22,36)(23,32)(24,38)(26,41)(27,43)(29,46)(30,47)(31,34)(33,37)(35,45)(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, 3780);