Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13364 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,27,29)(26,30,31,28)(33,37)(34,40)(35,42)(38,47)(39,46)(41,44)(43,45);(20,21)(22,23)(24,26,27,31)(25,28,29,30);(21,23)(32,33,36,39)(34,41,43,47)(35,44,42,38)(37,45,46,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6352);