Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623042 |
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×#554 |
1200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14645460, #14720073, #14720079, … |
| maximal normal subgroup of | #14645460, #14720073, #14720079, … |
| maximal quotient of | C2×#13071489, C2×#13071493, C2×C4⋊C4×C22⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18039);