Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C71 ⋊ #2402 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator, socle | C23×C71 | C24 |
| Frattini | C23 | C23×D71 |
| Fitting | C4×C4⋊C4×C71 | C2 |
| hypercenter | C4×C4⋊C4 | D71 |
| hypocenter | C71 | #2402 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
400 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 161 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=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^70,c^b=cg,h^b=h^701444 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31900588, #31900589, #31900593, … |
| maximal normal subgroup of | #31900588, #31900589, #31900593, … |
| maximal quotient of | #31919183, #31919184, #31919197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7818);