Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C19 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1134 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)(22,32)(23,28)(24,29)(25,30)(26,31)(27,34)(33,46)(35,47)(36,42)(37,51)(38,44)(39,45)(40,48)(41,50)(43,49);(20,22,26,35)(21,27,31,41)(23,33,24,37)(25,34,39,50)(28,40,29,43)(30,32,45,47)(36,48,38,49)(42,46,44,51);(20,23,26,24)(21,28,31,29)(22,33,35,37)(25,38,39,36)(27,40,41,43)(30,42,45,44)(32,46,47,51)(34,49,50,48);(20,24,26,23)(21,29,31,28)(22,33,35,37)(25,38,39,36)(27,40,41,43)(30,44,45,42)(32,46,47,51)(34,48,50,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26544);