Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
396 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)(20,21)(22,23)(24,25)(26,38)(27,45)(28,35)(29,34)(30,47)(31,50)(32,37)(33,40)(36,48)(39,41)(42,54)(43,46)(44,55)(49,53)(51,52);(24,26,32,44)(25,33,37,54)(27,46,34,52)(28,41,30,49)(29,40,45,42)(31,51,48,43)(35,38,47,55)(36,39,50,53);(21,23)(24,27,28,36,48,35,45,25,32,34,30,50,31,47,29,37)(26,39,40,46,51,54,49,55,44,53,42,52,43,33,41,38)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6434);