Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G | |
1042 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,25,27,39)(20,30)(21,35)(22,36)(26,41,42,49)(28,40,29,37)(32,46)(33,47)(34,45)(38,43,48,44);(18,19)(20,26)(21,25)(22,37)(23,28)(24,29)(27,31)(30,44)(32,38)(33,41)(34,43)(35,40)(36,39)(42,45)(46,48)(47,49);(18,20,31,45)(19,26,27,42)(21,32,36,46)(22,33,35,47)(23,34,24,30)(25,38,39,48)(28,43,29,44)(37,41,40,49);(18,21,24,22)(19,25,29,37)(20,32,30,33)(23,35,31,36)(26,38,44,41)(27,39,28,40)(34,47,45,46)(42,48,43,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10581);