Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
682 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)(26,34)(27,38)(28,43)(29,31)(30,35)(32,41)(33,40)(36,54)(37,51)(39,49)(42,50)(44,48)(45,53)(46,55)(47,52);(24,26,29,37)(25,30,31,45)(27,39,42,55)(28,44,40,36)(32,48,47,54)(33,49,43,46)(34,50,51,38)(35,52,53,41);(20,22,23,21)(24,25)(26,30)(27,32)(28,33)(29,31)(34,35)(36,46)(37,45)(38,41)(39,48)(40,43)(42,47)(44,49)(50,52)(51,53)(54,55);(25,31)(30,45)(32,47)(33,43)(34,51)(38,50)(46,49)(48,54)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26445);