Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D17 |
| Fitting | C22×C8×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D17 |
| commutator, hypocenter | C17 | C23×C8 |
| Frattini | C4 | C23×D17 |
| Fitting | C22×C8×C17 | C2 |
| socle | C23×C17 | C2×C4 |
| prime radical | C23×D17 | C4 |
| cosocle | C4×C17 | C24 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×#336, #14528479, D17×#340, … |
| maximal normal subgroup of | D17×#336, #14528479, D17×#340, … |
| maximal quotient of | C2×C4×C8×D17, C22×C8×Dic17, C2×C22⋊C8×D17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1305);