Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic34 |
| Sylow | C17 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D17 |
| commutator, socle, prime radical, cosocle | C22×C17 | C24 |
| Fitting | C4×Q8×C17 | C2 |
| hypercenter | C4×Q8 | D17 |
| hypocenter | C17 | Q82 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
185 conjugacy classes — view the full character table.
| maximal subgroup of | #14527861, #14527864, #14527923, … |
| maximal normal subgroup of | #14527861, #14527864, #14527923, … |
| maximal quotient of | Q8×#63225, C4⋊C4×Dic34, Q8×C4⋊Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1280);