Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33584 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
722 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)(21,23)(24,25)(26,36)(27,35)(28,31)(29,42)(30,33)(32,39)(34,44)(37,53)(38,52)(40,47)(41,49)(43,51)(45,50)(46,54)(48,55);(20,21,22,23)(25,31)(32,46)(33,35)(34,47)(36,52)(42,49)(48,51)(50,53);(24,26)(25,32)(27,37)(28,38)(29,43)(30,45)(31,46)(33,48)(34,50)(35,51)(36,42)(39,44)(40,54)(41,55)(47,53)(49,52);(24,27,28,30)(25,33,31,35)(26,37,38,45)(29,40,41,44)(32,48,46,51)(34,49,47,42)(36,50,52,53)(39,43,54,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26572);