Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33568 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C19 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C23×C19 ◁ C22×Q8×C19 ◁ G | |
1110 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)(22,31)(23,35)(24,27)(25,30)(26,33)(28,38)(29,40)(32,46)(34,48)(36,43)(37,45)(39,49)(41,47)(42,50)(44,51);(20,22)(21,26)(23,36)(24,39)(25,32)(27,42)(28,46)(29,44)(30,43)(31,35)(33,38)(34,40)(37,50)(41,51)(45,48)(47,49);(21,27)(24,40)(26,42)(28,47)(29,30)(31,48)(34,39)(35,45)(37,41)(43,44)(46,49)(50,51);(22,32)(26,43)(31,46)(33,36)(34,39)(42,44)(48,49)(50,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26556);