Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19×C32 · Schur multiplier (H2) = C2 |
| direct product | C19×#7458 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C19 | D4 |
| commutator | C4 | C2×C19×C32 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| socle, prime radical | C22×C19 | C4⋊C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C19 ◁ C4×C16×C19 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,25)(26,27)(28,29,30,34,31,35,38,44,32,36,39,45,41,47,50,54,33,37,40,46,42,48,51,55,43,49,52,56,53,57,58,59);(20,21,25,27,23,26,22,24)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 446);