Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C19×#2642 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
2286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4,5,6)(9,13)(11,14)(16,20)(21,23)(22,28)(29,30);(3,4,5,6)(7,8,10,12)(9,11,13,14)(15,16)(17,23)(18,22)(19,20)(21,25)(24,30)(26,29)(27,28);(3,4)(5,6)(7,9)(8,11)(10,13)(12,14)(15,17,19,25)(16,21,20,23)(18,26,27,24)(22,30,28,29);(15,18,19,27)(16,22,20,28)(17,24,25,26)(21,29,23,30)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27616);