Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#17986574 |
| Fitting | C2×C4⋊Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#536 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×C4⋊Q8×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C2×C4⋊Q8 | D71 |
| hypocenter | C71 | C2×#536 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
1512 conjugacy classes of subgroups.
1024 conjugacy classes — view the full character table.
| maximal subgroup of | #31889980, #31912968, #31912973, … |
| maximal normal subgroup of | #31889980, #31912968, #31912973, … |
| maximal quotient of | C2×#22590923, C2×#22590931, C2×#22590961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17828);