Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1953 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14556102 |
| commutator | C2×C4×C71 | C22×C4 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #405×C71 | C2 |
| socle | C2×C71 | #389 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #1953 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #405 | |
184 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 89 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=e,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^70,d^b=dg1432 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31914093, #31914096, #31914128, … |
| maximal normal subgroup of | #31914093, #31914096, #31914128, … |
| maximal quotient of | #31896063, #31896068, #31896073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5300);