Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
696 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)(29,34)(32,38)(33,39)(35,45)(36,42)(37,51)(40,44)(43,52)(46,50)(47,49)(48,53)(54,55);(25,30)(27,38)(28,39)(31,42)(32,33)(34,44)(36,50)(37,49)(40,52)(41,43)(45,53)(46,47)(48,55)(51,54);(20,22,23,21)(24,26)(25,31)(27,36)(28,37)(29,35)(30,42)(32,46)(33,47)(34,45)(38,50)(39,49)(40,48)(41,51)(43,54)(44,53)(52,55);(26,35)(31,45)(36,48)(37,49)(42,53)(46,54)(47,51)(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, 26442);