Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#10623026 |
| Fitting | C22×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ C2×#551 |
1328 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #14719962, #14719970, #14720042, … |
| maximal normal subgroup of | #14719962, #14719970, #14720042, … |
| maximal quotient of | C2×#13071461, C2×#13071465, C2×#13071470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 18007);