Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18377 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29)(22,31,32,44)(23,35,38,28)(25,30,39,27)(26,36,41,33)(34,46,47,51)(37,43,50,45)(40,49,42,48);(20,22)(21,26)(23,36)(24,32)(25,34)(27,42)(28,44)(29,41)(30,40)(31,35)(33,38)(37,49)(39,47)(43,46)(45,51)(48,50);(23,37)(28,45)(31,46)(33,48)(35,43)(36,49)(38,50)(44,51);(21,27)(22,32)(26,40)(28,43)(29,30)(31,46)(33,36)(34,47)(35,45)(41,42)(44,51)(48,49)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11365);