Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20986 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×Q8×C19 ◁ G | |
1718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(26,30,36,43)(27,31)(28,32)(29,33)(34,41,49,53)(35,42,51,55)(37,44)(38,45)(39,46)(40,47)(48,52,50,54);(24,26)(25,30,33,43)(27,34)(28,35)(29,36)(31,41,45,53)(32,42,47,55)(37,48)(38,49)(39,50)(40,51)(44,52,46,54);(21,23)(24,27,29,38)(25,31,33,45)(26,34,36,49)(28,39,40,37)(30,41,43,53)(32,46,47,44)(35,50,51,48)(42,54,55,52);(24,28,29,40)(25,32,33,47)(26,35,36,51)(27,37,38,39)(30,42,43,55)(31,44,45,46)(34,48,49,50)(41,52,53,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13974);