Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #459 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
414 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)(28,43)(29,45)(30,35)(31,37)(32,36)(33,44)(38,52)(40,51)(41,55)(42,47)(46,48)(49,53)(50,54);(24,26,28,37,30,38,44,29)(25,31,33,34,35,45,43,52)(27,36,40,53,42,54,41,46)(32,47,48,51,50,39,49,55);(24,27)(25,32)(26,36)(28,40)(29,46)(30,42)(31,47)(33,48)(34,51)(35,50)(37,53)(38,54)(39,45)(41,44)(43,49)(52,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5808);