Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #1451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D71 |
| commutator, socle | C22×C71 | C2×C42 |
| Fitting | C2×C4×C8×C71 | C2 |
| hypercenter | C2×C4×C8 | D71 |
| hypocenter | C71 | #1451 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C42 ◁ C2×C4×C8 | |
208 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 125 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^702296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31884345, #31884346, #31884351, … |
| maximal normal subgroup of | #31884345, #31884346, #31884351, … |
| maximal quotient of | #31886814, #31886834, #31887878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2799);