Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23903 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3485 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1744 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)(26,30,36,43)(27,31,38,45)(28,39,40,32)(34,46,48,41)(35,49,50,42)(37,44,51,52)(47,54,55,53);(20,21)(22,23)(24,26,29,36)(25,30,33,43)(27,34,38,48)(28,35,40,50)(31,41,45,46)(32,42,39,49)(37,47,51,55)(44,53,52,54);(21,23)(24,27)(25,31)(26,34)(28,37)(29,38)(30,41)(32,44)(33,45)(35,47)(36,48)(39,52)(40,51)(42,53)(43,46)(49,54)(50,55);(24,28)(25,32)(26,35)(27,37)(29,40)(30,42)(31,44)(33,39)(34,47)(36,50)(38,51)(41,53)(43,49)(45,52)(46,54)(48,55)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16893);