Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#3633 |
| Fitting | Q8×C17 ⋊ C8 |
| Sylow | C17 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#3633 |
| commutator, socle | C2×C17 | C22×C8 |
| Fitting | Q8×C17 | C8 |
| prime radical | C2×D17 | C22×C4 |
| cosocle | C2×#595 | C23 |
| hypercenter | Q8 | #3633 |
| hypocenter | C17 | C8×Q8 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 136 |
50 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#3633, Q16×#3633, SD16⋊#3633, … |
| maximal normal subgroup of | SD16×#3633, Q16×#3633, SD16⋊#3633, … |
| maximal quotient of | C4⋊C4×#3633, #14545931, #14545933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1664);