Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
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)(20,23,27,33)(21,26)(22,25)(24,28,32,29)(30,31)(34,35)(36,44)(37,48,50,41)(38,51)(39,43)(40,46)(42,53)(45,58,61,65)(47,59)(49,56,52,57)(54,60,64,62)(55,63);(18,20)(19,23,25,33)(21,29)(22,27)(24,31,32,26)(28,30)(34,36,38,46,39,47,53,63)(35,40,42,44,43,55,51,59)(37,45,52,62,50,61,49,60)(41,54,57,58,48,64,56,65);(18,20)(19,24)(21,29)(22,27)(23,31)(25,32)(26,33)(28,30)(34,37)(35,41)(36,45)(38,52)(39,50)(40,54)(42,57)(43,48)(44,58)(46,62)(47,61)(49,53)(51,56)(55,64)(59,65)(60,63)629 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2357);