Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2913 |
476 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 293 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=eg,e^2=g,b^a=be,e^a=eg,h^a=h^10,d^c=dg244 conjugacy classes — view the full character table.
| maximal subgroup of | #14670303, #14670307, #14670310, … |
| maximal normal subgroup of | #14670303, #14670307, #14670310, … |
| maximal quotient of | #14722767, #14722824, #14722911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13110);