Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11035 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1238 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)(24,25,29,34,30,33,28,45)(26,35,38,50,39,31,37,47)(27,40,44,51,42,32,43,49)(36,46,54,48,53,52,41,55);(24,26,30,39)(25,31,33,35)(27,41,42,54)(28,38,29,37)(32,48,40,55)(34,50,45,47)(36,44,53,43)(46,51,52,49);(21,23)(24,27)(25,32)(26,36)(28,44)(29,43)(30,42)(31,46)(33,40)(34,51)(35,52)(37,54)(38,41)(39,53)(45,49)(47,55)(48,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4023);