Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
456 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)(22,23,28,33)(24,34,37,52)(25,29,27,31)(26,39,42,49)(30,45,48,35)(32,38,50,40)(36,46,43,51)(41,47,53,44);(23,29)(24,35)(25,27)(26,40)(30,46)(31,33)(32,50)(34,44)(36,41)(37,45)(38,42)(43,53)(47,52)(48,51);(19,21)(22,24,25,36,28,37,27,43)(23,30,31,47,33,48,29,44)(26,41,38,35,42,53,40,45)(32,46,49,34,50,51,39,52)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6402);