Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32941 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#32943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1316 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)(24,25,30,35)(26,36,40,46)(27,41,43,49)(28,34,29,33)(31,39,47,38)(32,44,48,42)(37,51,53,45)(50,54,55,52);(24,26,29,39,30,40,28,38)(25,31,34,46,35,47,33,36)(27,37,44,54,43,53,42,52)(32,45,49,55,48,51,41,50);(24,27)(25,32)(26,37)(28,42)(29,44)(30,43)(31,45)(33,41)(34,49)(35,48)(36,50)(38,52)(39,54)(40,53)(46,55)(47,51);(21,23)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25931);