Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33587 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
712 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)(26,34)(27,37)(28,39)(30,42)(32,47)(33,46)(35,52)(36,51)(38,41)(40,50)(43,54)(44,55)(45,53)(48,49);(20,21,22,23)(24,25)(26,30)(27,32)(28,33)(29,31)(34,42)(35,44)(36,43)(37,47)(38,48)(39,46)(40,45)(41,49)(50,53)(51,54)(52,55);(24,26,29,36)(25,30,31,43)(27,38,40,52)(28,41,39,35)(32,48,45,55)(33,49,46,44)(34,50,51,37)(42,53,54,47);(25,31)(30,43)(32,45)(33,46)(42,54)(44,49)(47,53)(48,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26575);