Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C19 · Schur multiplier (H2) = C28 |
| direct product | C22×C19×#336 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C4×C19 | C22 |
| commutator | C2 | C22×C4×C8×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C25×C19 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4×C19 ◁ G | |
3086 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4);(5,6)(7,8)(13,14,15,17,16,18,19,20);(6,8)(9,10,11,12)3040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13320);