Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C71 ⋊ C8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C2×C71 | C2×C4×C8 |
| Fitting | C2×C4⋊C8×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×C4⋊C8 | D71 |
| hypocenter | C71 | C8×C4⋊C4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4⋊C8 | |
296 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 165 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=e,b^2=f,c^2=de,e^2=g,b^a=bd,h^a=h^70,h^b=h^70,h^c=h^701480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31888213, #31888219, #31888220, … |
| maximal normal subgroup of | #31888213, #31888219, #31888220, … |
| maximal quotient of | C4⋊C8×C71⋊C8, #31888584, #31888601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4375);