Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8325 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#11007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| 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)(24,25)(26,35)(27,40,43,49)(28,44)(29,33)(30,34)(31,37)(32,42,47,41)(36,45,53,55)(38,46)(39,48)(50,52,54,51);(20,21)(22,23)(24,26,30,39)(25,31,34,46)(27,36,43,53)(28,38,29,37)(32,45,47,55)(33,48,44,35)(40,50,49,54)(41,52,42,51);(21,23)(24,27)(25,32)(26,36)(28,42)(29,41)(30,43)(31,45)(33,49)(34,47)(35,50)(37,52)(38,51)(39,53)(40,44)(46,55)(48,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3995);