Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1942 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)(26,35)(27,32)(28,33)(29,42)(30,34)(31,37)(36,51)(38,45)(39,48)(40,50)(41,49)(43,46)(44,54)(47,52)(53,55);(24,26)(25,31)(27,36)(28,37)(29,43)(30,38)(32,47)(33,45)(34,46)(35,42)(39,52)(40,54)(41,53)(44,49)(48,55)(50,51);(21,23)(24,27,30,41)(25,32,34,49)(26,36,38,53)(28,40,29,39)(31,44,46,47)(33,50,42,48)(35,51,45,55)(37,54,43,52);(24,28,30,29)(25,33,34,42)(26,37,38,43)(27,39,41,40)(31,45,46,35)(32,48,49,50)(36,52,53,54)(44,51,47,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16391);