Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C2×C19×#1353 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C19 |
| prime radical | C24×C19 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C19 ◁ C22×C4⋊C4×C19 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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);(4,7,8,9)(11,12,14,18,15,17,21,24)(13,16,20,22,19,23,26,25);(3,4)(5,9)(6,8)(7,10)(11,13)(12,16,17,23)(14,20)(15,19)(18,25,24,22)(21,26)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4707);