Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | #536×C71 ⋊ C2 |
| Sylow | C71 ⋊ #3028 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#14556096 |
| commutator | C23×C71 | C24 |
| Frattini | C23 | C23×D71 |
| Fitting | #536×C71 | C2 |
| socle | C2×C71 | C2×#120 |
| hypercenter | #536 | D71 |
| hypocenter | C71 | #3028 |
| LCS | G ▷ C23×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #536 | |
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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=g,d^2=g,b^a=be,c^a=cf,d^a=dg,f^b=fg,e^c=eg,h^c=h^70799 conjugacy classes — view the full character table.
| maximal subgroup of | #31916440, #31916441, #31916447, … |
| maximal normal subgroup of | #31916440, #31916441, #31916447, … |
| maximal quotient of | #31971488, #31971490, #31971495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13915);