Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#10622602 |
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×#385 |
1232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #14649151, #14649171, C4×#10622602, … |
| maximal normal subgroup of | #14649151, #14649171, C4×#10622602, … |
| maximal quotient of | C2×(C2×D11)⋊#95, C2×#13066847, C2×#13066848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6919);