Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#19422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,23)(24,25)(26,27)(28,31)(29,32)(30,34)(33,37)(35,39)(36,38)(40,41);(18,19,23,25,21,24,20,22)(26,28)(27,31)(29,36)(30,35)(32,38)(33,40)(34,39)(37,41);(19,24)(22,25)(27,32)(29,37)(31,38)(33,34)(36,41)(39,40);(28,35)(31,39)(36,41)(38,40)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12410);