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×#33841 |
| 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 | |
690 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)(24,25,29,34)(26,35,36,47)(27,40,43,49)(28,31,42,33)(30,45,46,38)(32,50,52,41)(37,53,54,48)(39,55,44,51);(24,26,29,36)(25,30,34,46)(27,37,43,54)(28,44,42,39)(31,48,33,53)(32,51,52,55)(35,49,47,40)(38,50,45,41);(21,23)(26,36)(30,46)(35,47)(37,54)(38,45)(39,44)(48,53)(51,55);(25,31)(26,37)(27,41)(28,42)(30,47)(33,34)(35,46)(36,54)(38,39)(40,49)(43,50)(44,45)(48,51)(53,55)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26829);