Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
996 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)(22,23)(24,25,29,34,30,35,28,33)(26,31,38,47,39,48,37,46)(27,40,42,50,43,51,44,32)(36,52,53,49,41,55,54,45);(21,23)(24,26,29,38,30,39,28,37)(25,31,34,47,35,48,33,46)(27,41,42,54,43,36,44,53)(32,49,40,55,50,45,51,52);(24,27,30,43)(25,32,35,50)(26,36,39,41)(28,42,29,44)(31,45,48,49)(33,40,34,51)(37,53,38,54)(46,52,47,55);(21,23)(24,28,30,29)(25,33,35,34)(26,37,39,38)(27,42,43,44)(31,46,48,47)(32,40,50,51)(36,53,41,54)(45,52,49,55)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18131);