Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13039 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #442 |
| 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 | |
472 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)(24,25,30,36,40,55,28,47,32,38,29,49,31,37,48,35)(26,39,41,53,50,34,46,52,43,54,45,33,42,51,27,44);(20,21,22,23)(24,26,40,42,32,43,31,50)(25,33,37,44,38,53,55,52)(27,28,45,29,46,48,41,30)(34,36,54,35,51,49,39,47);(24,27)(25,34)(26,28)(29,42)(30,50)(31,41)(32,46)(33,36)(35,44)(37,54)(38,51)(39,55)(40,45)(43,48)(47,52)(49,53)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6027);