Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C11⋊C32 |
| derived, Sylow | C11 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D11 |
| commutator, hypocenter | C11 | C22×C32 |
| Frattini | C16 | C22×D11 |
| Fitting | C22×C11×C16 | C2 |
| socle, prime radical | C23×C11 | C16 |
| cosocle | C11×C16 | C23 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14641459, #14641460, #14641471, … |
| maximal normal subgroup of | #14641459, #14641460, #14641471, … |
| maximal quotient of | C2×C4×C11⋊C32, C2×C22⋊(C11⋊C32), C2×C4⋊(C11⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6799);