Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C19×#2251 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 57 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(4,6)(7,8,12,16)(9,17,19,31)(10,22,24,37)(11,25,23,15)(13,26,27,20)(14,29,30,18)(21,36,35,33)(28,34,32,38);(7,9,18,34,11,21,24,26,12,19,29,38,23,35,10,20)(8,13,22,33,15,28,30,31,16,27,37,36,25,32,14,17);(3,4,5,6)(9,19)(13,27)(17,31)(20,26)(21,35)(28,32)(33,36)(34,38)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26703);