Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3287 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29,34,38)(30,39,40,56)(31,36,33,48)(32,44,47,57)(35,50,51,42)(37,43,55,46)(41,58,49,54)(45,52,59,53);(20,22)(21,24)(23,27)(25,26)(30,40)(35,51)(39,56)(41,49)(42,50)(45,59)(52,53)(54,58);(28,30,34,40)(29,35,38,51)(31,41,33,49)(32,45,47,59)(36,52,48,53)(37,54,55,58)(39,57,56,44)(42,43,50,46);(22,27)(24,26)(28,31,34,33)(29,36,38,48)(30,41,40,49)(32,43,47,46)(35,52,51,53)(37,44,55,57)(39,58,56,54)(42,45,50,59)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26872);