Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 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)(24,32,35,28)(25,29)(26,31)(27,30)(33,50,51,42)(34,48,39,43)(36,53,52,44)(37,46)(38,45)(40,49)(41,47);(22,24)(23,28)(25,36)(26,39)(27,35)(29,44)(30,32)(31,48)(33,37)(34,41)(38,52)(40,51)(42,46)(43,47)(45,53)(49,50);(19,21)(22,25,27,38)(23,29,30,45)(24,33,35,51)(26,40,41,37)(28,42,32,50)(31,49,47,46)(34,52,39,36)(43,53,48,44)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4001);