Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33613 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(26,36,39,52)(27,42,43,32)(28,46,48,53)(30,49,47,35)(31,50,45,40)(33,51,38,37)(41,55,54,44);(24,26,37,42,30,41,48,50,29,39,51,32,47,54,28,40)(25,31,46,44,35,27,38,52,34,45,53,55,49,43,33,36);(21,23)(24,27)(25,32)(26,38)(28,44)(29,43)(30,45)(31,47)(33,39)(34,42)(35,40)(36,51)(37,52)(41,53)(46,54)(48,55)(49,50);(26,39)(27,43)(31,45)(32,42)(36,52)(40,50)(41,54)(44,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26601);