Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1318 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)(27,41)(28,44)(29,33)(30,34)(31,38)(32,42)(36,40)(37,46)(39,47)(43,48)(45,49)(50,52)(51,54)(53,55);(24,26,30,40)(25,31,34,47)(27,37,43,53)(28,39,29,38)(32,46,49,55)(33,36,44,35)(41,50,48,51)(42,54,45,52);(21,23)(24,25)(26,36)(27,32)(28,33)(29,44)(30,34)(31,38)(35,40)(37,51)(39,47)(41,42)(43,49)(45,48)(46,54)(50,53)(52,55);(24,27,30,43)(25,32,34,49)(26,37,40,53)(28,45,29,42)(31,46,47,55)(33,48,44,41)(35,50,36,51)(38,54,39,52)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17449);