Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#13281 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 63 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,30)(27,28)(29,31)(32,33)(34,44)(35,41)(36,51)(37,53)(38,43)(39,46)(40,49)(42,52)(45,58)(47,54)(48,60)(50,57)(55,62)(56,61)(59,63);(21,23)(25,28)(29,30)(32,34,35,45,37,47,49,61,38,48,50,62,52,63,36,46)(33,39,51,59,42,55,57,60,43,56,40,54,53,58,41,44);(24,26,27,31)(25,29,28,30)(32,35,37,49,38,50,52,36)(33,40,42,41,43,51,53,57)(34,45,47,61,48,62,63,46)(39,54,55,44,56,59,58,60)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6269);