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×#33851 |
| 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 | |
674 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)(26,34)(27,39)(28,42)(31,35)(32,51)(33,47)(37,38)(40,44)(41,53)(43,45)(46,52)(49,55)(50,54);(24,25,29,33)(26,35,38,54)(27,40,43,51)(28,44,42,32)(30,45,47,39)(31,48,50,36)(34,46,37,55)(41,52,53,49);(21,23);(24,26,29,38)(25,31,33,50)(27,41,43,53)(28,34,42,37)(30,46,47,55)(32,52,44,49)(35,51,54,40)(36,45,48,39)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26839);