Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #1851 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C22×C4 |
| Fitting | C22×M16×C71 | C2 |
| hypercenter | C22×M16 | D71 |
| hypocenter | C71 | #1851 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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,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 | #31891553, #31891554, #31891560, … |
| maximal normal subgroup of | #31891553, #31891554, #31891560, … |
| maximal quotient of | #31891297, #31891302, #31891308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4693);