Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2931 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D11 |
| commutator, socle | C22×C11 | C23×C4 |
| Fitting, prime radical | C11×#532 | C2 |
| cosocle | C2×C4×C11 | C24 |
| hypercenter | #532 | D11 |
| hypocenter | C11 | #2931 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^10,d^b=dg,h^c=h^10196 conjugacy classes — view the full character table.
| maximal subgroup of | #14644778, #14644779, #14644788, … |
| maximal normal subgroup of | #14644778, #14644779, #14644788, … |
| maximal quotient of | #14724289, #14724297, #14724305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13222);