Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(19,20)(22,23)(24,29)(25,30)(26,43)(27,44)(28,33)(31,40)(32,41)(34,52)(35,48)(36,53)(37,46)(38,50)(39,47)(42,51)(45,49);(18,19)(20,21)(22,24,28,38)(23,29,33,50)(25,39,42,36)(26,34,40,35)(27,45,41,37)(30,47,51,53)(31,48,43,52)(32,46,44,49);(18,20,21,19)(23,30)(24,34)(25,40)(26,42)(27,41)(29,46)(31,32)(33,51)(35,38)(36,45)(37,39)(43,44)(48,52)(49,50)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6400);