Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11485 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #99 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C2×M16 | C23×C19 |
| socle | C2×C19 | #1459 |
| prime radical | C19×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C2×C8×C19 ◁ C2×C19×#131 ◁ G | |
372 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)(20,21,25,31,26,30,42,48,27,32,43,50,24,40,34,49)(22,33,36,51,35,28,23,29,37,45,38,46,41,44,39,47);(20,22)(21,28)(23,34)(24,41)(25,38)(26,35)(27,37)(29,31)(30,45)(32,44)(33,40)(36,43)(39,42)(46,48)(47,50)(49,51);(20,23,26,38,27,39,24,36)(21,29,30,46,32,47,40,51)(22,34,35,25,37,42,41,43)(28,31,45,48,44,50,33,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4473);