Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C181 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | #10624382 |
| commutator, hypocenter | C181 | C128 |
| Fitting | C32×C181 | C4 |
| socle, prime radical | C2×C181 | C64 |
| cosocle | #26040998 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C32 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
Polycyclic presentation:
2^7,181|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^162,h^b=h^1801568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19325);