Finite Group DatabasebetaFinite Group Databasebeta| order | 4768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D149⋊C16 |
| derived, Sylow | C149 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #10597010 |
| commutator, hypocenter | C149 | C2×C16 |
| Frattini | C4 | C2×#10597010 |
| Fitting | C8×C149 | C4 |
| socle | C2×C149 | C2×C8 |
| prime radical | C2×D149 | C8 |
| cosocle | #11924746 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2384 |
Polycyclic presentation:
2^5,149|a^2=c,c^2=d,d^2=e,f^a=f^105,f^b=f^148,f^c=f^148328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4768, 219);