Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12503 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#12522 |
| 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 | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 65 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)(34,35)(36,44)(37,40)(38,51)(39,52)(41,47)(42,45)(43,50)(46,56)(48,63)(49,64)(53,61)(54,60)(55,65)(57,59)(58,62);(18,20,27,31,22,29,21,28)(19,23,30,33,25,32,24,26)(35,40)(41,53)(42,54)(43,52)(44,56)(51,64)(55,57)(58,63);(34,36,45,59,39,48,49,61,37,46,60,65,50,62,38,47)(35,41,51,58,43,55,54,56,40,53,64,63,52,57,42,44)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5510);