Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #2396 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14648860, #14648862, #14648865, … |
| maximal normal subgroup of | #14648860, #14648862, #14648865, … |
| maximal quotient of | #14675483, #14675496, #14675517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 7778);