Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| 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 | |
1270 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)(24,25,29,33,30,35,28,34)(26,36,38,31,40,47,39,46)(27,41,43,32,44,49,42,50)(37,45,52,51,54,48,53,55);(24,26)(25,31)(27,37)(28,39)(29,38)(30,40)(32,48)(33,47)(34,36)(35,46)(41,51)(42,53)(43,52)(44,54)(45,50)(49,55);(21,23)(24,27,30,44)(25,32,35,50)(26,37,40,54)(28,43,29,42)(31,45,46,48)(33,41,34,49)(36,51,47,55)(38,53,39,52)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3993);