Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D181⋊C64 |
| derived, Sylow | C181 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10624382 |
| commutator, hypocenter | C181 | C2×C64 |
| Frattini | C16 | C2×#10624382 |
| Fitting | C32×C181 | C4 |
| socle | C2×C181 | C2×C32 |
| prime radical | C2×D181 | C32 |
| cosocle | #19153722 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C32 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^162,h^b=h^180,h^c=h^1801568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19678);