Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10622538 |
| Sylow | C11 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14643154, #14643155, #14643158, … |
| maximal normal subgroup of | #14643154, #14643155, #14643158, … |
| maximal quotient of | C2×#13068362, C2×C4×C22⋊(C11⋊C8), C2×C4×C4⋊(C11⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13126);