Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #2587 |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=efg,c^2=g,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×#2587, C2×#13074031, #14924127, … |
| maximal normal subgroup of | D11×#2587, C2×#13074031, #14924127, … |
| maximal quotient of | #14676243, #14676396, #14677603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9925);