Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C11×C22⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #2557 |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=efg,d^2=f,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×#2557, C2×#13073709, #14923957, … |
| maximal normal subgroup of | D11×#2557, C2×#13073709, #14923957, … |
| maximal quotient of | #14676112, #14676396, #14677011, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9603);