Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #342×C211 ⋊ C2 |
| Sylow | C211 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6752 |
Polycyclic presentation:
2^7,211|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,d^b=dg,h^c=h^2102354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 4297);