Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C22×C4 |
| Fitting | C2×#97×C71 | C2 |
| hypercenter | C2×#97 | D71 |
| hypocenter | C71 | #1917 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 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=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^70,c^b=cg1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1917×D71, C2×#22588904, #31999514, … |
| maximal normal subgroup of | #1917×D71, C2×#22588904, #31999514, … |
| maximal quotient of | #31895597, #31895604, #31895611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5074);