Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
894 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)(20,21)(22,25)(23,26)(24,27)(28,34)(29,32)(30,33)(31,35)(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);(20,22)(21,25)(23,28)(24,29)(26,31)(27,32)(30,35)(33,34)(36,38)(37,43)(39,49)(40,50)(41,55)(42,51)(44,56)(45,48)(46,61)(47,57)(52,63)(53,65)(54,64)(58,66)(59,67)(60,62);(20,23)(21,26)(22,28)(24,30)(25,31)(27,33)(29,35)(32,34)(36,39,42,53)(37,44,47,59)(38,49,51,65)(40,54,41,52)(43,56,57,67)(45,60,46,58)(48,62,61,66)(50,64,55,63);(21,27)(25,32)(26,33)(31,34)(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, 11443);