Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C8 |
| direct product | C17×#12523 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C17 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C82×C17 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25)(20,26,29,33)(21,30,27,24)(23,31,32,28)(35,39)(36,43)(37,44)(40,45)(41,49)(42,48)(46,47);(18,20,27,31,22,29,21,28)(19,23,30,33,25,32,24,26);(34,35,40,49,37,41,36,39,38,42,43,47,44,46,45,48)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5511);