Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2481 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=ef,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^10238 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2481, C2×#13072871, #14921542, … |
| maximal normal subgroup of | D11×#2481, C2×#13072871, #14921542, … |
| maximal quotient of | #14675774, #14675977, #14676805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 8765);