Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,28)(23,31)(24,26)(25,30)(27,33)(29,35)(32,34)(36,37)(38,46)(39,42)(40,44)(41,45)(43,47)(48,51)(49,50);(20,22)(21,25)(23,32)(24,29)(26,34)(27,35)(28,31)(30,33)(37,42)(39,40)(43,50)(44,45)(46,51)(47,48);(36,38)(37,43)(39,47)(40,48)(41,49)(42,50)(44,46)(45,51);(21,26)(22,29)(27,31)(30,32)(36,39,41,40)(37,44,45,42)(38,47,49,48)(43,46,51,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11646);