Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#10623367 |
| Fitting | C2×C11×H(5,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ C2×#577 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
214 conjugacy classes — view the full character table.
| maximal subgroup of | #14769683, #14769689, #14769710, … |
| maximal normal subgroup of | #14769683, #14769689, #14769710, … |
| maximal quotient of | C2×#13077142, C2×#13077146, C2×#13077209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19270);