Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C181 ⋊ C4 |
| Sylow | C181 ⋊ #1402 |
122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2896 |
Polycyclic presentation:
2^7,181|a^2=d,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^162,d^b=deg,e^b=eg,f^b=fg,d^c=dfg,e^c=eg,e^d=eg,h^d=h^180782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19629);