Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1864 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,32,27,33,26,44)(22,34,36,48,38,45,37,49)(23,39,42,31,24,28,40,30)(29,41,46,35,47,43,50,51);(21,28,33,39)(23,40)(24,42)(25,26)(29,45,47,34)(30,32,31,44)(35,41)(36,37)(43,51)(46,48,50,49);(20,22)(21,29)(23,41)(24,43)(25,37)(26,36)(27,38)(28,45)(30,48)(31,49)(32,50)(33,47)(34,39)(35,40)(42,51)(44,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5937);