Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C8×D4×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3341 |
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|a^2=eg,b^2=g,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^70,d^b=de,f^c=fg,h^c=h^701435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31911063, #31911067, #31911091, … |
| maximal normal subgroup of | #31911063, #31911067, #31911091, … |
| maximal quotient of | #32013719, #32015110, #32015597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 16933);