Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #2399 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #398×C71 | C2 |
| hypercenter | #398 | D71 |
| hypocenter | C71 | #2399 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #398 | |
504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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=e,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^70,h^d=h^70814 conjugacy classes — view the full character table.
| maximal subgroup of | #31907828, #31908265, #31969814, … |
| maximal normal subgroup of | #31907828, #31908265, #31969814, … |
| maximal quotient of | #31919192, #31919195, #31919205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7802);