Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
692 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)(26,34)(27,33)(28,42)(30,31)(32,37)(35,47)(36,48)(38,51)(40,41)(43,45)(46,50)(49,55)(52,54);(24,26)(25,32)(27,35)(28,43)(29,34)(30,45)(31,36)(33,46)(37,42)(38,52)(39,47)(40,54)(41,49)(44,48)(50,51)(53,55);(21,23)(24,27,31,41)(25,33,30,40)(26,35,36,49)(28,38,42,51)(29,39,44,53)(32,46,45,54)(34,47,48,55)(37,50,43,52);(24,28)(25,29)(26,36)(27,38)(30,44)(31,42)(33,39)(34,43)(35,49)(37,48)(40,53)(41,51)(47,52)(50,55)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26821);