Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1980 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30)(23,27)(24,36)(25,29)(26,32)(28,38)(31,46)(33,44)(34,42)(35,50)(37,40)(39,51)(41,48)(43,49)(45,47);(20,22)(21,26)(23,31)(24,37)(25,33)(27,41)(28,44)(29,40)(30,36)(32,38)(34,47)(35,51)(39,42)(43,45)(46,50)(48,49);(20,23)(21,27)(22,31)(24,35)(25,34)(26,39)(28,43)(29,42)(30,45)(32,48)(33,47)(36,50)(37,51)(38,49)(40,41)(44,46);(23,34)(27,42)(31,47)(35,49)(39,41)(43,50)(45,46)(48,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16402);