Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C2×C19×#1814 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | #380 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1330 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);(3,4)(5,14)(6,19,21,26)(7,22)(8,12)(9,13)(10,16)(11,20,27,23)(15,24,31,34)(17,25)(18,29)(28,30,33,32);(3,5,7,16,9,18,8,17)(4,10,12,14,13,25,22,29)(6,15,20,30,21,31,23,32)(11,24,26,28,27,34,19,33);(3,6)(4,11)(5,15)(7,20)(8,23)(9,21)(10,24)(12,26)(13,27)(14,28)(16,30)(17,32)(18,31)(19,22)(25,34)(29,33)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13662);