Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,30,43,29,34,28,33)(26,31,44,55,37,47,36,46)(27,38,40,32,42,49,41,50)(35,51,52,45,39,54,53,48);(21,23)(24,26,28,36,29,37,30,44)(25,31,33,46,34,47,43,55)(27,39,41,52,42,35,40,53)(32,48,38,54,50,45,49,51);(24,27)(25,32)(26,35)(28,40)(29,42)(30,41)(31,45)(33,49)(34,50)(36,52)(37,39)(38,43)(44,53)(46,54)(47,48)(51,55);(21,23)(24,28,29,30)(25,33,34,43)(26,36,37,44)(27,40,42,41)(31,46,47,55)(32,49,50,38)(35,52,39,53)(45,54,48,51)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18133);