Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11663 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12738 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#102 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×C17×#135 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
926 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)(22,23,25,29,27,32,39,31)(24,33,36,47,37,50,34,49)(26,40,38,30,42,46,51,48)(28,41,44,35,45,52,43,53);(22,24)(23,28)(25,34)(26,41)(27,37)(29,43)(30,47)(31,44)(32,45)(33,46)(35,51)(36,39)(38,53)(40,50)(42,52)(48,49);(19,21)(22,25,27,39)(23,29,32,31)(24,34,37,36)(26,38,42,51)(28,43,45,44)(30,46,48,40)(33,49,50,47)(35,41,53,52)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5726);