Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33496 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C24 |
| commutator | C2 | C23×C16×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C23×C8 |
| prime radical | C23×C19 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,38,41,39,42,44,47,40,43,45,48,46,49,50,51);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34);(21,27)(25,28)(26,35)(33,34)2584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26484);