Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1146 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)(24,37)(25,29)(26,34)(28,40)(31,38)(32,48)(33,44)(35,45)(36,43)(39,42)(41,50)(46,49)(47,51);(20,21)(22,31,33,26)(23,27)(24,28)(25,29)(30,34,44,38)(32,47,49,41)(35,42)(36,43)(37,40)(39,45)(46,51,48,50);(20,22)(21,26)(23,32)(24,38)(25,33)(27,41)(28,44)(29,31)(30,37)(34,40)(35,51)(36,49)(39,50)(42,46)(43,47)(45,48);(20,23,25,36)(21,27,29,43)(22,32,33,49)(24,39,40,35)(26,41,31,47)(28,45,37,42)(30,46,44,48)(34,51,38,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16987);