Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C11×M16 ⋊ C2 |
| Sylow | C11 ⋊ #2875 |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^10,d^c=dg,h^d=h^10268 conjugacy classes — view the full character table.
| maximal subgroup of | #14650583, #14650587, #14650590, … |
| maximal normal subgroup of | #14650583, #14650587, #14650590, … |
| maximal quotient of | #14719367, #14719388, #14719447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12939);