Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C2×C19×#1609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
1060 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(4,8)(5,6)(9,10)(11,12,15,18)(13,16,20,23)(14,17,21,24)(19,25,26,22);(3,4)(5,8)(6,10)(7,9)(11,13)(12,16)(14,19)(15,20)(17,22)(18,23)(21,26)(24,25);(3,5,7,6)(4,8,9,10)(11,14)(12,17)(13,19)(15,21)(16,22)(18,24)(20,26)(23,25)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11093);