Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#21785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2308 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1262 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)(18,19)(20,30,34,25)(21,27,22,36)(23,29)(24,28)(26,35,44,37)(31,47)(32,41)(33,46,38,42)(39,45)(40,48)(43,49);(18,20)(19,25)(21,31)(22,32)(23,38)(24,34)(26,43)(27,41)(28,30)(29,46)(33,39)(35,49)(36,47)(37,48)(40,44)(42,45);(18,21,24,22)(19,26,28,44)(20,31,34,32)(23,37,39,35)(25,40,30,43)(27,29,36,45)(33,49,38,48)(41,42,47,46);(18,22,24,21)(19,27,28,36)(20,32,34,31)(23,37,39,35)(25,41,30,47)(26,29,44,45)(33,49,38,48)(40,42,43,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14773);