Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16×C19 · Schur multiplier (H2) = C25 |
| direct product | C16×#41×C19 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C16×C19 | C22 |
| commutator | C2 | C23×C16×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C23×C8 |
| prime radical | C2×#41×C19 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C16×C19 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(17,18)(19,22)(20,21)(23,24);(18,21)(22,24);(17,19,20,23)(18,22,21,24)3040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26466);