Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C181 ⋊ #1384 |
132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^1802552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2611);