Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#20399 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C22 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1442 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,35)(27,32)(28,33)(29,43)(30,34)(31,38)(36,49)(37,50)(39,45)(40,46)(41,48)(42,47)(44,52)(51,55)(53,54);(24,26,29,39,30,38,28,37)(25,31,33,45,34,35,43,50)(27,36,40,51,41,52,42,53)(32,44,47,55,48,49,46,54);(20,22,23,21)(24,27,30,41)(25,32,34,48)(26,36,38,52)(28,42,29,40)(31,44,35,49)(33,47,43,46)(37,53,39,51)(45,55,50,54);(24,28,30,29)(25,33,34,43)(26,37,38,39)(27,40,41,42)(31,45,35,50)(32,46,48,47)(36,51,52,53)(44,54,49,55)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13387);