Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#20593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×C17×2−1+4 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×#41×C17 ◁ G | |
3594 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)(22,23,26,31,27,30,39,44)(24,32,34,45,35,28,38,41)(25,29,37,43,36,42,49,52)(33,46,48,53,47,40,50,51);(22,24,27,35)(23,28,30,32)(25,33,36,47)(26,38,39,34)(29,40,42,46)(31,45,44,41)(37,50,49,48)(43,53,52,51);(19,21)(22,25)(23,29)(24,33)(26,37)(27,36)(28,40)(30,42)(31,43)(32,46)(34,48)(35,47)(38,50)(39,49)(41,51)(44,52)(45,53);(25,36)(29,42)(33,47)(37,49)(40,46)(43,52)(48,50)(51,53)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13581);