Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1706 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)(24,25,29,33)(26,30,35,45)(27,37,38,49)(28,40,43,32)(31,42,47,39)(34,50,51,54)(36,48,41,46)(44,53,55,52);(20,21)(22,23)(24,26,29,35)(25,30,33,45)(27,34,38,51)(28,41,43,36)(31,44,47,55)(32,48,40,46)(37,54,49,50)(39,53,42,52);(21,23)(24,27)(25,31)(26,34)(28,42)(29,38)(30,44)(32,49)(33,47)(35,51)(36,53)(37,40)(39,43)(41,52)(45,55)(46,54)(48,50);(26,35)(28,43)(30,45)(32,40)(34,51)(37,49)(39,42)(44,55)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16902);