Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1690 |
152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=df,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^10,e^c=eg,h^c=h^10118 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1690, C2×#13068109, #14736381, … |
| maximal normal subgroup of | D11×#1690, C2×#13068109, #14736381, … |
| maximal quotient of | #14646871, #14650000, #14650004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4003);