Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C4⋊Q8×D17 |
| Fitting | C17×C4⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ C2×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C24 |
| Fitting | C17×C4⋊Q8 | C2 |
| prime radical | C22×D17 | C23 |
| hypercenter | C4⋊Q8 | D17 |
| hypocenter | C17 | C2×C4⋊Q8 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#332, D17×#333, #14527454, … |
| maximal normal subgroup of | D17×#332, D17×#333, #14527454, … |
| maximal quotient of | D17×#384, D17×#389, D17×#391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1090);