Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#18306 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1040 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)(21,26)(22,30)(23,34)(27,39)(28,37)(29,35)(32,46)(33,44)(36,45)(38,41)(40,49)(42,51)(43,48)(47,50);(20,21)(22,27)(23,35)(24,29)(25,28)(26,34)(30,41)(31,40)(32,47)(33,42)(36,49)(37,45)(38,48)(39,46)(43,51)(44,50);(23,36)(26,37)(32,43)(34,45)(35,49)(38,39)(46,48)(47,51);(20,22,31,44)(21,27,40,50)(23,32,45,46)(24,33,25,30)(26,38,49,51)(28,41,29,42)(34,48,36,43)(35,47,37,39)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11294);