Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23444 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1994 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)(26,30)(27,31)(28,32)(29,33)(34,41)(35,42)(36,43)(37,45)(38,46)(39,47)(40,48)(44,50)(49,53)(51,54)(52,55);(24,26,29,36)(25,30,33,43)(27,34,38,50)(28,39,40,35)(31,44,46,41)(32,47,48,42)(37,51,52,49)(45,53,55,54);(21,23)(24,27)(25,31)(26,34)(28,37)(29,38)(30,41)(32,45)(33,46)(35,49)(36,50)(39,51)(40,52)(42,53)(43,44)(47,54)(48,55);(24,28,29,40)(25,32,33,48)(26,35,36,39)(27,37,38,52)(30,42,43,47)(31,45,46,55)(34,49,50,51)(41,53,44,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16434);