Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
974 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)(18,19,21,20)(22,23,27,32)(24,33,37,29)(25,38,40,47)(26,28,42,31)(30,41,46,39)(34,43,36,45)(35,50,51,53)(44,49,48,52);(18,20,21,19)(23,28)(24,34)(26,42)(30,38)(31,32)(35,49)(36,37)(39,41)(43,45)(46,47)(50,53)(51,52);(19,20)(22,24,27,37)(23,29,32,33)(25,35,40,51)(26,36,42,34)(28,43,31,45)(30,44,46,48)(38,53,47,50)(39,49,41,52);(22,25)(23,30)(24,35)(26,41)(27,40)(28,38)(29,44)(31,47)(32,46)(33,48)(34,49)(36,52)(37,51)(39,42)(43,53)(45,50)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18174);