Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#23045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
844 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)(20,21,23,22)(24,25,29,34,30,35,28,33)(26,36,39,31,40,46,38,47)(27,32,43,50,44,51,42,49)(37,48,52,45,53,55,41,54);(20,22,23,21)(24,26)(25,31)(27,41)(28,39)(29,38)(30,40)(32,48)(33,46)(34,36)(35,47)(37,42)(43,53)(44,52)(45,49)(50,54)(51,55);(24,26)(25,31)(27,37)(28,38)(29,39)(30,40)(32,45)(33,36)(34,46)(35,47)(41,42)(43,52)(44,53)(48,49)(50,55)(51,54);(24,27,29,43,30,44,28,42)(25,32,34,50,35,51,33,49)(26,37,39,52,40,53,38,41)(31,45,46,55,47,54,36,48)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16033);