Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23494 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1362 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)(21,22)(24,25)(26,30)(27,37)(28,40)(29,33)(31,39)(32,43)(34,51)(35,49)(36,46)(38,50)(41,45)(42,48)(44,53)(47,54)(52,55);(20,21)(22,23)(24,26,29,36)(25,30,33,46)(27,34,38,52)(28,41,43,35)(31,47,48,44)(32,49,40,45)(37,51,50,55)(39,54,42,53);(20,22,23,21)(24,27)(25,31)(26,34)(28,42)(29,38)(30,44)(32,50)(33,48)(35,54)(36,52)(37,40)(39,43)(41,53)(45,55)(46,47)(49,51);(27,38)(31,48)(34,52)(37,50)(39,42)(44,47)(51,55)(53,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16482);