Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D149⋊C64 |
| derived, Sylow | C149 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10597010 |
| commutator, hypocenter | C149 | C2×C64 |
| Frattini | C16 | C2×#10597010 |
| Fitting | C32×C149 | C4 |
| socle | C2×C149 | C2×C32 |
| prime radical | C2×D149 | C32 |
| cosocle | #18011817 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9536 |
Polycyclic presentation:
2^7,149|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^105,h^b=h^148,h^c=h^1481312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 19678);