Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C11×#386 ⋊ C2 |
| Sylow | C11 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,b^a=be,c^a=cf,d^b=de,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | D4×C22⋊C4×D11, C2×#13071434, #14912973, … |
| maximal normal subgroup of | D4×C22⋊C4×D11, C2×#13071434, #14912973, … |
| maximal quotient of | #14675172, #14675174, #14675187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7328);