Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2491 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg,h^b=h^10,h^c=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | #14821807, #14821811, #14821867, … |
| maximal normal subgroup of | #14821807, #14821811, #14821867, … |
| maximal quotient of | #14675727, #14676126, #14676872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 8876);