Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#106 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C24×C17 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
414 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)(24,33,36,50,37,51,34,48)(26,40,38,30,42,47,52,49)(28,43,45,35,46,41,44,53);(22,24,27,37)(23,28)(25,34,39,36)(26,41,42,43)(29,44)(30,48)(31,45)(32,46)(33,40)(35,52,53,38)(47,51)(49,50);(19,21)(22,25,27,39)(23,29,32,31)(24,34,37,36)(26,38,42,52)(28,44,46,45)(30,47,49,40)(33,48,51,50)(35,43,53,41)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5918);