Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#10622724 |
| Fitting | C23×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ C2×#435 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14644326, #14644328, #14646672, … |
| maximal normal subgroup of | #14644326, #14644328, #14646672, … |
| maximal quotient of | C2×#13067445, C2×#13067459, C2×#13067452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13189);