Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33854 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C19×#443 ◁ G | |
656 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)(21,27)(22,32)(23,35)(24,25)(28,45)(29,47)(30,49)(31,44)(33,50)(34,40)(36,41)(38,39)(42,46)(43,48);(20,21)(22,28)(23,36)(24,30)(25,41)(26,31)(27,35)(29,33)(32,46)(34,47)(37,42)(38,44)(39,49)(40,43)(45,50)(48,51);(20,22)(21,28)(23,33)(24,40)(25,32)(26,34)(27,42)(29,36)(30,43)(31,47)(35,37)(38,51)(39,50)(41,46)(44,48)(45,49);(20,22)(21,29)(23,37)(24,32)(25,40)(26,34)(27,43)(28,36)(30,42)(31,45)(33,35)(38,50)(39,51)(41,48)(44,46)(47,49)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26842);