Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13334 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 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)(22,33)(23,27)(24,40)(25,43)(26,31)(28,34)(29,37)(30,41)(32,39)(35,48)(36,45)(38,47)(42,50)(44,49)(46,51);(21,27)(23,37)(24,41)(25,39)(28,33)(29,32)(30,43)(31,40)(34,42)(35,44)(38,51)(45,46)(47,48)(49,50);(20,22)(21,28)(23,38)(24,42)(25,44)(26,36)(27,45)(29,48)(30,49)(31,46)(32,50)(33,40)(34,41)(35,39)(37,51)(43,47)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6322);