Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#135 ⋊ C2 |
| Sylow | C11 ⋊ #3284 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^10,e^d=eg175 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3284, C2×#13080340, #15629062, … |
| maximal normal subgroup of | D11×#3284, C2×#13080340, #15629062, … |
| maximal quotient of | #14744556, #14744561, #14744571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16234);