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×#13388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
396 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)(22,23,27,32)(24,28,36,45)(25,29,40,48)(26,41,39,31)(30,49,47,38)(33,43,35,44)(34,52,37,46)(42,53,50,51);(18,19)(20,21)(22,24)(23,28)(25,37)(26,33)(27,36)(29,46)(30,50)(31,44)(32,45)(34,40)(35,39)(38,53)(41,43)(42,47)(48,52)(49,51);(18,20,21,19)(23,29)(24,33)(25,38)(26,39)(28,42)(30,31)(32,48)(34,37)(35,36)(40,49)(41,47)(43,52)(44,46)(45,50)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6376);