Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #339×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D71 |
| commutator | C4×C71 | C2×C42 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #339×C71 | C2 |
| socle | C22×C71 | C4×D4 |
| hypercenter | #339 | D71 |
| hypocenter | C71 | #1764 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #339 | |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^701036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1764×D71, C2×#22588174, #31995295, … |
| maximal normal subgroup of | #1764×D71, C2×#22588174, #31995295, … |
| maximal quotient of | #31888123, #31888133, #31888140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4344);