Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#10587467 |
| derived, Sylow | C17 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #595 |
| commutator, hypocenter | C17 | C2×C32 |
| Frattini | C8 | C2×#595 |
| Fitting | C2×C8×C17 | C4 |
| socle, prime radical | C22×C17 | C16 |
| cosocle | #63214 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10587467, #14543889, #14543891, … |
| maximal normal subgroup of | C4×#10587467, #14543889, #14543891, … |
| maximal quotient of | C4×#10587467, C22⋊#10587467, C4⋊#10587467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1479);