Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13260 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #459 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
482 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)(21,23)(24,25,28,33,46,34,44,50,30,36,43,32,29,35,27,42)(26,37,38,52,39,47,54,49,41,53,55,48,40,51,45,31);(20,21,22,23)(24,26)(25,31)(27,38)(28,45)(29,39)(30,41)(32,47)(33,51)(34,48)(35,52)(36,49)(37,42)(40,46)(43,54)(44,55)(50,53);(24,27,29,43,30,44,46,28)(25,32,34,42,36,33,35,50)(26,38,39,54,41,55,40,45)(31,47,48,37,49,51,52,53)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6248);