Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C22×C19×D16 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
718 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)(20,21,23,22)(24,25)(26,31)(27,30)(28,41)(29,32)(33,38)(34,39)(35,47)(36,42)(37,51)(40,43)(44,52)(45,50)(46,49)(48,54)(53,55);(25,30)(27,38)(28,39)(31,42)(32,43)(33,34)(36,50)(37,49)(40,52)(41,44)(45,46)(47,54)(48,55)(51,53);(20,22,23,21)(24,26)(25,31)(27,36)(28,37)(29,35)(30,42)(32,47)(33,45)(34,46)(38,50)(39,49)(40,48)(41,51)(43,54)(44,53)(52,55);(25,32)(26,35)(30,43)(33,44)(34,41)(36,48)(37,49)(50,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26444);