Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(23,30)(25,31)(26,33)(28,34)(36,37,42,47)(38,48,51,61)(39,44,53,59)(40,46,41,45)(43,55,57,50)(49,62,65,66)(52,60,54,58)(56,63,67,64);(20,21)(22,25)(23,26)(24,27)(28,32)(29,31)(30,33)(34,35)(36,38,42,51)(37,43,47,57)(39,49,53,65)(40,50,41,55)(44,56,59,67)(45,48,46,61)(52,63,54,64)(58,66,60,62);(20,22)(21,25)(23,28)(24,29)(26,32)(27,31)(30,34)(33,35)(36,39)(37,44)(38,49)(40,54)(41,52)(42,53)(43,56)(45,60)(46,58)(47,59)(48,62)(50,64)(51,65)(55,63)(57,67)(61,66);(20,23,24,30)(21,26,27,33)(22,28,29,34)(25,32,31,35)(36,40,42,41)(37,45,47,46)(38,50,51,55)(39,52,53,54)(43,48,57,61)(44,58,59,60)(49,63,65,64)(56,66,67,62)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11453);