Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#97 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,33,43,52,44,53,30,35,27,32,29,34,45,54)(26,36,38,48,46,51,41,31,40,47,37,55,39,50,42,49);(20,21,22,23)(24,26)(25,31)(27,41)(28,42)(29,46)(30,40)(32,50)(33,51)(34,55)(35,49)(36,53)(37,44)(38,45)(39,43)(47,54)(48,52);(24,26)(25,31)(27,42)(28,41)(29,46)(30,40)(32,51)(33,50)(34,55)(35,49)(36,54)(37,45)(38,44)(39,43)(47,53)(48,52)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6014);