Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(24,25,30,35)(26,36,39,54)(27,31,29,33)(28,41,44,51)(32,47,50,37)(34,40,52,42)(38,48,45,53)(43,49,55,46);(25,31)(26,37)(27,29)(28,42)(32,48)(33,35)(34,52)(36,46)(38,43)(39,47)(40,44)(45,55)(49,54)(50,53);(21,23)(24,26,27,38,30,39,29,45)(25,32,33,49,35,50,31,46)(28,43,40,37,44,55,42,47)(34,48,51,36,52,53,41,54)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6402);