Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C2×C19×#2221 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(4,10)(5,16)(6,11)(7,8)(12,27)(13,24)(14,23)(15,25)(17,31)(18,21)(19,20)(22,28)(29,34)(30,33);(3,4,11,24,8,14,20,25,9,15,19,23,7,13,6,10)(5,12,26,27,16,28,31,33,18,29,32,34,21,30,17,22);(3,5)(4,12)(6,17)(7,21)(8,16)(9,18)(10,22)(11,26)(13,30)(14,28)(15,29)(19,32)(20,31)(23,34)(24,27)(25,33)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26602);