Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D173⋊C64 |
| derived, Sylow | C173 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10621924 |
| commutator, hypocenter | C173 | C2×C64 |
| Frattini | C16 | C2×#10621924 |
| Fitting | C32×C173 | C4 |
| socle | C2×C173 | C2×C32 |
| prime radical | C2×D173 | C32 |
| cosocle | #19149585 | C22 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11072 |
Polycyclic presentation:
2^7,173|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^80,h^b=h^172,h^c=h^1721504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19678);