Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #399×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2539 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #399×C71 | C2 |
| hypercenter | #399 | D71 |
| hypocenter | C71 | #2539 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #399 | |
900 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 159 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=eg,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^70,h^d=h^70808 conjugacy classes — view the full character table.
| maximal subgroup of | #31907927, #31908329, #31971559, … |
| maximal normal subgroup of | #31907927, #31908329, #31971559, … |
| maximal quotient of | #31919672, #31920205, #31920557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 9437);