Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C4⋊C4×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2406 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | C22×C4⋊C4×C71 | C2 |
| hypercenter | C22×C4⋊C4 | D71 |
| hypocenter | C71 | #2406 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
864 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^70,c^b=cg1438 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31895254, #31895256, #31895274, … |
| maximal normal subgroup of | #31895254, #31895256, #31895274, … |
| maximal quotient of | #31919343, #31920137, #31920233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 7845);