Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #2326 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | C2×#124×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×#124 | D71 |
| hypocenter | C71 | #2326 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^70,c^b=ce,h^b=h^701024 conjugacy classes — view the full character table.
| maximal subgroup of | #31912624, #31912644, #31913445, … |
| maximal normal subgroup of | #31912624, #31912644, #31913445, … |
| maximal quotient of | #31918715, #31918757, #31918764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7223);