Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8803 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#8804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #383 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #126 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,29,31,33)(23,25)(24,28)(26,30,34,35)(27,32)(36,37)(38,46,48,51)(39,43,49,42)(40,44)(41,45)(47,50);(21,25,28,27)(26,29,34,33)(36,38,47,49,41,48,40,39)(37,42,44,46,45,43,50,51);(20,22,23,30,24,31,32,35)(21,26,27,33,28,34,25,29)(36,39,40,48,41,49,47,38)(37,43,44,51,45,42,50,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1792);