Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#388 ⋊ C2 |
| Sylow | C11 ⋊ #2367 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^10,d^b=de,h^c=h^10,h^d=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2367, C2×#13071690, #14913386, … |
| maximal normal subgroup of | D11×#2367, C2×#13071690, #14913386, … |
| maximal quotient of | #14675216, #14675316, #14675336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7584);