Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13331 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13332 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #459 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
566 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)(26,36)(27,32)(28,34)(29,45)(30,35)(31,38)(33,42)(37,46)(39,51)(40,53)(41,52)(43,49)(44,50)(47,55)(48,54);(21,23)(24,26,30,40)(25,31,35,48)(27,41,44,55)(28,37,29,39)(32,36,50,53)(33,51,49,46)(34,52,45,47)(38,43,54,42);(25,32)(26,37)(27,42)(28,29)(31,46)(33,34)(35,50)(36,52)(38,54)(39,40)(43,44)(45,49)(47,53)(48,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6320);