Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C71 ⋊ #1444 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D71 |
| commutator | C23×C71 | C22×C4 |
| Fitting | C2×#95×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C2×#95 | D71 |
| hypocenter | C71 | #1444 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
608 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 229 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=d,c^2=e,b^a=bd,c^a=ce,h^a=h^70,c^b=cf1444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31891501, #31891502, #31891515, … |
| maximal normal subgroup of | #31891501, #31891502, #31891515, … |
| maximal quotient of | #31885380, #31906056, #31906060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2775);