Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C19 · Schur multiplier (H2) = C42 |
| direct product | C19×#12594 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | C42 |
| commutator | C4 | C2×C4×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#97 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,32,38,33,35,40,42,34,39,41,43,31,37,30,36);(21,24)(25,27)(29,35,39,37)(30,40)(32,41)(36,43,42,38);(20,22,23,26)(21,25,24,27)(28,30,31,41,34,40,33,32)(29,36,37,43,39,42,35,38)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5582);