Finite Group DatabasebetaFinite Group Databasebeta| order | 1088 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#63216 |
| derived, Sylow | C17 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #595 |
| commutator, hypocenter | C17 | C22×C16 |
| Frattini | C4 | C22×#595 |
| Fitting | C22×C4×C17 | C4 |
| socle, prime radical | C23×C17 | C8 |
| cosocle | #3622 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #14543822, #14543823, #14543838, … |
| maximal normal subgroup of | #14543822, #14543823, #14543838, … |
| maximal quotient of | C2×C4×#63216, C2×C22⋊#63216, C2×C4⋊#63216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1088, 1602);