Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10783 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #386 |
| 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 ◁ C23×C4×C17 ◁ 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)(20,24,29,38)(21,31,33,41)(22,27)(23,26)(25,32,39,34)(28,42)(30,37,45,49)(35,40)(36,46)(43,48)(44,47);(18,20)(19,24,26,38)(21,28)(22,30)(23,29)(25,36,39,47)(27,37,40,49)(31,42,41,48)(32,44)(33,43)(34,46)(35,45);(18,21)(19,25)(20,28)(22,34)(23,33)(24,36)(26,39)(27,41)(29,43)(30,46)(31,40)(32,35)(37,48)(38,47)(42,49)(44,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3771);