Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33848 |
| 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 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
696 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)(24,25,29,33)(26,34,38,53)(27,39,42,52)(28,43,41,31)(30,45,47,36)(32,49,51,40)(35,48,54,46)(37,55,44,50);(24,26,29,38)(25,30,33,47)(27,35,42,54)(28,44,41,37)(31,48,43,46)(32,50,51,55)(34,52,53,39)(36,49,45,40);(21,23);(25,31)(26,35)(27,40)(28,41)(30,34)(32,51)(33,43)(36,37)(38,54)(42,49)(44,45)(46,55)(47,53)(48,50)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26836);