Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #2336 |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2336, C2×#13071415, #14912697, … |
| maximal normal subgroup of | D11×#2336, C2×#13071415, #14912697, … |
| maximal quotient of | #14675045, #14675091, #14675099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7309);