Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#7167 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | D4 |
| commutator | C4 | C4×C16×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| socle, prime radical | C23×C19 | C22⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ C2×C4×C8×C19 ◁ G | |
286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 2 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(25,29)(26,27)(30,31)(32,33,35,40,37,34,39,43,38,42,36,41,46,45,47,44);(21,23)(24,25,27,30,28,31,26,29)(32,34,36,44,37,42,47,40,38,45,35,43,46,33,39,41)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 155);