Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#451 ⋊ C2 |
| Sylow | C11 ⋊ #3225 |
376 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,d^b=dg,h^b=h^10,f^c=fg,h^c=h^10121 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3225, C2×#13079731, #15625181, … |
| maximal normal subgroup of | D11×#3225, C2×#13079731, #15625181, … |
| maximal quotient of | #14763154, #14763547, #14764387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15625);