Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23440 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1898 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)(26,36)(27,41)(28,35)(29,34)(30,33)(31,38)(32,43)(37,52)(39,47)(40,48)(42,49)(44,50)(45,51)(46,54)(53,55);(21,23)(24,26)(25,31)(27,42)(28,39)(29,38)(30,40)(32,49)(33,47)(34,48)(35,36)(37,44)(41,52)(43,54)(45,53)(46,51)(50,55);(24,27,30,45)(25,32,33,50)(26,37,40,54)(28,44,29,43)(31,46,47,52)(34,51,35,41)(36,49,48,55)(38,42,39,53);(25,33)(31,47)(32,50)(34,35)(36,48)(41,51)(46,52)(49,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16428);