Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #344×C71 ⋊ C2 |
| Sylow | C71 ⋊ #2048 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17985917 |
| commutator | C22×C4×C71 | C23 |
| Frattini | C22×C4 | C22×D71 |
| Fitting | #344×C71 | C2 |
| socle | C2×C71 | #394 |
| hypercenter | #344 | D71 |
| hypocenter | C71 | #2048 |
| LCS | G ▷ C22×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #344 | |
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,71|c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^70,c^b=cf,d^b=dg,h^b=h^70,f^c=fg,h^c=h^70793 conjugacy classes — view the full character table.
| maximal subgroup of | #2048×D71, C2×#22589616, #32025299, … |
| maximal normal subgroup of | #2048×D71, C2×#22589616, #32025299, … |
| maximal quotient of | #31901021, #31901028, #31901035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 5786);