Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13310 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13310 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
552 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)(24,32)(25,30)(26,31)(28,35)(29,37)(34,48)(36,47)(38,43)(39,42)(40,46)(41,49)(44,51)(45,50);(21,27)(23,37)(24,25)(28,44)(29,32)(30,43)(31,42)(33,48)(34,49)(35,40)(38,39)(41,46)(45,47)(50,51);(20,22)(21,28)(23,34)(24,40)(25,35)(26,36)(27,41)(29,45)(30,47)(31,46)(32,33)(37,49)(38,51)(39,50)(42,44)(43,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6298);