Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #342×C71 ⋊ C2 |
| Sylow | C71 ⋊ #1867 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14556098 |
| commutator | C23×C71 | C22×C4 |
| Frattini | C24 | C22×D71 |
| Fitting | #342×C71 | C2 |
| socle | C22×C71 | #120 |
| hypercenter | #342 | D71 |
| hypocenter | C71 | #1867 |
| LCS | G ▷ C23×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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=f,b^2=f,b^a=bd,c^a=ce,h^a=h^70,e^b=eg,d^c=dg,h^c=h^70802 conjugacy classes — view the full character table.
| maximal subgroup of | #1867×D71, C2×#22588622, #31998536, … |
| maximal normal subgroup of | #1867×D71, C2×#22588622, #31998536, … |
| maximal quotient of | #31891419, #31891424, #31891429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 4792);