Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C24×C4×D11 |
| Fitting | C24×C4×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D11 |
| commutator, hypocenter | C11 | C25×C4 |
| Frattini | C2 | C25×D11 |
| Fitting | C24×C4×C11 | C2 |
| socle | C25×C11 | C22 |
| prime radical | C25×D11 | C2 |
| cosocle | C2×C11 | C26 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C22⋊#95, C2×(C2×D11)⋊#95, #14674978, … |
| maximal normal subgroup of | D11×C22⋊#95, C2×(C2×D11)⋊#95, #14674978, … |
| maximal quotient of | C23×C42×D11, C24×C4×Dic11, C23×C22⋊C4×D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19299);