Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(21,24)(22,25)(26,32)(27,30)(28,31)(29,33)(34,35,40,45)(36,46,49,59)(37,42,51,57)(38,44,39,43)(41,53,55,48)(47,60,63,64)(50,58,52,56)(54,61,65,62);(18,20)(19,23)(21,26)(22,27)(24,29)(25,30)(28,33)(31,32)(34,36)(35,41)(37,47)(38,48)(39,53)(40,49)(42,54)(43,46)(44,59)(45,55)(50,61)(51,63)(52,62)(56,64)(57,65)(58,60);(18,21)(19,24)(20,26)(22,28)(23,29)(25,31)(27,33)(30,32)(34,37,40,51)(35,42,45,57)(36,47,49,63)(38,52,39,50)(41,54,55,65)(43,58,44,56)(46,60,59,64)(48,62,53,61);(19,25)(23,30)(24,31)(29,32)(34,38,40,39)(35,43,45,44)(36,48,49,53)(37,50,51,52)(41,46,55,59)(42,56,57,58)(47,61,63,62)(54,64,65,60)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11443);