Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #1280 |
264 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 97 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=d,b^2=e,d^2=g,b^a=bc,c^a=cf,h^a=h^70,d^b=df1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884197, #31884198, #31884199, … |
| maximal normal subgroup of | #31884197, #31884198, #31884199, … |
| maximal quotient of | #31883982, #31883984, #31883990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2353);