Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#12660 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #117 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | #432 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×#97 ◁ G | |
330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,34)(27,39)(28,33)(29,31)(30,36)(32,40)(35,43)(37,44)(38,47)(41,53)(42,45)(46,49)(48,51)(50,55)(52,54);(21,23)(24,26,27,37,28,38,41,52,29,36,40,51,42,35,49,50)(25,30,32,44,33,43,46,54,31,34,39,48,45,47,53,55);(25,31)(26,35,36,38)(27,40)(30,43,34,47)(33,45)(37,52,51,50)(41,49)(44,55,48,54)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5648);