Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×#595 |
| Fitting | C16×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #595 |
| commutator, hypocenter | C17 | C4×C16 |
| Frattini | C8 | C2×#595 |
| Fitting | C16×C17 | C4 |
| socle | C2×C17 | C4×C8 |
| prime radical | C2×D17 | C2×C8 |
| cosocle | C8×D17 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C16 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#595, #14543890, C2×C16×#595, … |
| maximal normal subgroup of | C32×#595, #14543890, C2×C16×#595, … |
| maximal quotient of | C16×#3624, #14543698, #14543821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1433);