Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C11×#494 ⋊ C2 |
| Sylow | C11 ⋊ #1722 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^10,c^b=cf,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14667190, D11×#1722, C2×#13068288, … |
| maximal normal subgroup of | #14667190, D11×#1722, C2×#13068288, … |
| maximal quotient of | #14647563, #14653570, #14653577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4182);