Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,27)(20,28,30,32)(21,24,22,26)(25,31,33,29)(34,35)(36,39)(37,40)(38,41)(42,45)(43,46)(44,48)(47,49);(19,24)(21,22)(25,28)(26,27)(29,31)(32,33)(34,36,38,43)(35,39,41,46)(37,42,44,49)(40,47,48,45);(18,20,23,30)(19,25,27,33)(21,29,22,31)(24,32,26,28)(34,37)(35,40)(36,42)(38,44)(39,45)(41,48)(43,49)(46,47)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2947);