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×#21783 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2308 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
1230 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)(20,29,32,24)(21,33,35,26)(22,28)(23,27)(25,31,41,36)(30,38)(34,47,49,42)(37,39)(40,44)(43,45)(46,48);(18,20)(19,24)(21,30)(22,36)(23,32)(25,39)(26,38)(27,29)(28,41)(31,37)(33,43)(34,48)(35,45)(40,47)(42,46)(44,49);(18,20)(19,25)(21,30)(22,36)(23,32)(24,28)(26,40)(27,41)(29,39)(31,37)(33,46)(34,48)(35,45)(38,42)(43,47)(44,49);(18,21,23,35)(19,26,27,33)(20,30,32,45)(22,34,37,49)(24,38,29,43)(25,40,41,46)(28,42,39,47)(31,44,36,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14771);