Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×M32×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D71 |
| commutator, socle | C22×C71 | C22×C8 |
| Fitting | C2×M32×C71 | C2 |
| hypercenter | C2×M32 | D71 |
| hypocenter | C71 | #2113 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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,e^2=f,f^2=g,b^a=bd,h^a=h^70,c^b=cg,h^b=h^701456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884796, #31912901, #31912905, … |
| maximal normal subgroup of | #31884796, #31912901, #31912905, … |
| maximal quotient of | #31906518, #31906590, #31906659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6125);