Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#448 ⋊ C2 |
| Sylow | C11 ⋊ #3271 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=g,c^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^10,d^b=de,e^b=eg,h^c=h^10,e^d=eg,h^d=h^10124 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3271, C2×#13080204, #15628852, … |
| maximal normal subgroup of | D11×#3271, C2×#13080204, #15628852, … |
| maximal quotient of | #14743228, #14743348, #14743573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16098);