Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11074 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,29,35,30,34,28,33)(26,31,37,45,38,46,43,50)(27,39,41,32,42,49,40,48)(36,51,52,47,53,55,54,44);(20,21,22,23)(24,26)(25,31)(27,36)(28,43)(29,37)(30,38)(32,47)(33,50)(34,46)(35,45)(39,51)(40,54)(41,52)(42,53)(44,48)(49,55);(24,27,30,42)(25,32,34,48)(26,36,38,53)(28,41,29,40)(31,44,46,47)(33,49,35,39)(37,54,43,52)(45,55,50,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4062);