Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8603 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11259 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #117 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #382 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×#117 ◁ G | |
590 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)(24,25)(26,34,37,30)(27,38,40,53)(28,33)(29,32)(31,39,44,54)(35,48)(36,47,51,43)(41,45)(42,49)(46,55)(50,52);(20,21)(22,23)(24,26,28,36,29,37,41,51)(25,30,33,43,32,34,45,47)(27,35,39,49,40,50,54,55)(31,42,38,52,44,46,53,48);(21,23)(24,27)(25,31,32,44)(26,35)(28,39)(29,40)(30,42,34,46)(33,38,45,53)(36,49)(37,50)(41,54)(43,52,47,48)(51,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4247);