Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7172 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C19 | D8 |
| commutator | C8 | C4×C8×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| socle | C22×C19 | #340 |
| prime radical | C23×C19 | #103 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,23,26,24,27,22,25)(28,29,32,37,34,40,46,39)(30,41,43,55,45,56,57,50)(31,38,33,36,47,53,48,54)(35,44,49,58,52,59,51,42);(21,25,27,26)(28,30,33,44,32,43,47,58,34,45,48,59,46,57,31,42)(29,35,38,50,39,51,54,56,40,52,53,55,37,49,36,41)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 160);