Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1290 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^10,d^b=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14640458, #14640459, #14640461, … |
| maximal normal subgroup of | #14640458, #14640459, #14640461, … |
| maximal quotient of | #14640311, #14640319, #14640360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2380);