Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
820 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)(18,19,22,27,23,28,38,26)(20,29,32,24,34,30,33,40)(21,35,36,25,37,41,49,42)(31,45,46,43,48,39,47,44);(18,20,22,32,23,34,38,33)(19,24,26,29,28,40,27,30)(21,31,36,46,37,48,49,47)(25,39,35,43,42,45,41,44);(18,19)(20,30)(21,25)(22,26)(23,28)(24,32)(27,38)(29,34)(31,44)(33,40)(35,36)(37,42)(39,46)(41,49)(43,48)(45,47);(18,21,22,36,23,37,38,49)(19,25,26,35,28,42,27,41)(20,31,32,46,34,48,33,47)(24,39,29,43,40,45,30,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17796);