Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33527 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1098 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)(26,35)(27,32)(28,41)(29,39)(30,34)(31,37)(33,43)(36,52)(38,53)(40,50)(42,46)(44,51)(45,49)(47,55)(48,54);(24,26,30,38)(25,31,34,48)(27,36,29,45)(28,42,44,55)(32,46,39,47)(33,49,50,52)(35,51,53,41)(37,40,54,43);(21,23)(24,25)(26,31)(27,39)(28,33)(29,32)(30,34)(35,37)(36,47)(38,48)(40,51)(41,43)(42,49)(44,50)(45,46)(52,55)(53,54);(24,27,30,29)(25,32,34,39)(26,36,38,45)(28,40,44,43)(31,46,48,47)(33,41,50,51)(35,52,53,49)(37,42,54,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26515);