Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11084 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #127 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #399 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
878 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)(21,23)(24,25,29,34,30,35,28,33)(26,31,39,47,37,45,38,46)(27,32,42,50,41,49,43,51)(36,52,40,55,53,44,54,48);(20,21,22,23)(24,26)(25,31)(27,40,41,54)(28,38)(29,39)(30,37)(32,48,49,55)(33,46)(34,47)(35,45)(36,42,53,43)(44,50,52,51);(24,27)(25,32)(26,36)(28,43)(29,42)(30,41)(31,44)(33,51)(34,50)(35,49)(37,53)(38,54)(39,40)(45,52)(46,55)(47,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4072);