Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#106 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C23×C19 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
294 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)(26,34,36,50)(27,38)(28,31)(29,43)(30,35,45,51)(32,41)(33,42)(37,52,44,48)(39,46,54,49)(40,53)(47,55);(24,26,29,44,28,36,42,37)(25,30,33,49,31,45,43,46)(27,39,41,35,40,54,55,51)(32,48,38,34,47,52,53,50);(20,21,22,23)(25,31)(30,45)(32,47)(33,43)(34,50)(38,53)(46,49)(48,52)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6172);