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×#33853 |
| 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) = 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)(25,30)(26,35)(27,36)(28,37)(31,42)(32,38)(33,48)(34,46)(40,41)(43,53)(44,45)(47,52)(49,55)(51,54);(24,25,29,33)(26,31,35,34)(27,38,40,54)(28,42,44,46)(30,45,48,37)(32,50,51,39)(36,47,41,55)(43,52,53,49);(21,23)(24,26,29,35)(25,31,33,34)(27,36,40,41)(28,37,44,45)(30,46,48,42)(32,49,51,52)(38,47,54,55)(39,53,50,43);(24,27,29,40)(25,32,33,51)(26,36,35,41)(28,43,44,53)(30,47,48,55)(31,49,34,52)(37,39,45,50)(38,46,54,42)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26841);