Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C71 ⋊ Q8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator | C22×C71 | C23×C4 |
| Fitting | #380×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #380 | D71 |
| hypocenter | C71 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #380 | |
820 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 253 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=e,d^2=e,b^a=be,c^a=cf,d^b=de,h^d=h^701030 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31893889, #31893893, #31893917, … |
| maximal normal subgroup of | #31893889, #31893893, #31893917, … |
| maximal quotient of | #31918864, #31918871, #31918936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7342);