Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#452 ⋊ C2 |
| Sylow | C11 ⋊ #3212 |
400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^10,c^b=ce,h^b=h^10,f^c=fg127 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3212, C2×#13079595, #15625004, … |
| maximal normal subgroup of | D11×#3212, C2×#13079595, #15625004, … |
| maximal quotient of | #14763102, #14763470, #14764315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15489);