Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#496 ⋊ C2 |
| Sylow | C11 ⋊ #3264 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^b=h^10,h^c=h^10,e^d=eg,h^d=h^10109 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3264, C2×#13080095, #15628853, … |
| maximal normal subgroup of | D11×#3264, C2×#13080095, #15628853, … |
| maximal quotient of | #14743119, #14743239, #14743359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15989);