Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#20986 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×Q8×C17 ◁ G | |
1718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,28,34,41)(25,29)(26,30)(27,31)(32,39,47,51)(33,40,49,53)(35,42)(36,43)(37,44)(38,45)(46,50,48,52);(22,24)(23,28,31,41)(25,32)(26,33)(27,34)(29,39,43,51)(30,40,45,53)(35,46)(36,47)(37,48)(38,49)(42,50,44,52);(19,21)(22,25,27,36)(23,29,31,43)(24,32,34,47)(26,37,38,35)(28,39,41,51)(30,44,45,42)(33,48,49,46)(40,52,53,50);(22,26,27,38)(23,30,31,45)(24,33,34,49)(25,35,36,37)(28,40,41,53)(29,42,43,44)(32,46,47,48)(39,50,51,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13974);