Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21775 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C17×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×#41×C17 ◁ G | |
1362 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(18,19)(20,24)(21,23)(22,25)(26,27,30,34,31,29,38,33)(28,32,37,40,36,35,41,39);(18,20)(19,22)(21,25)(23,24)(26,28)(27,32)(29,35)(30,37)(31,36)(33,39)(34,40)(38,41);(20,25)(22,24)(26,29)(27,31)(28,35)(30,33)(32,36)(34,38)(37,39)(40,41);(19,23)(22,24)(28,36)(32,35)(37,41)(39,40)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14763);