Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43×C19 · Schur multiplier (H2) = C24×C42 |
| direct product | C2×C4×C19×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C19 | C22 |
| commutator | C2 | C2×C43×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C19 ◁ G | |
1790 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4,5,6);(11,12,13,16,14,15,17,18);(7,8,9,10)(12,15)(16,18)3040 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13314);