Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11092 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #124 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #394 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
882 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)(24,25,29,35,30,34,28,33)(26,31,39,47,38,48,37,46)(27,40,44,32,42,50,43,49)(36,51,53,45,41,54,52,55);(24,26)(25,31)(27,41,42,36)(28,37)(29,39)(30,38)(32,45,49,55)(33,46)(34,48)(35,47)(40,51,50,54)(43,53,44,52);(21,23)(24,27)(25,32)(26,36)(28,44)(29,43)(30,42)(31,45)(33,50)(34,49)(35,40)(37,53)(38,41)(39,52)(46,54)(47,51)(48,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4080);