Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #2979 |
| 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 | #2979 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
410 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 205 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,f^2=g,b^a=be,d^a=de,h^a=h^10,c^b=ce,d^b=dg,d^c=dg190 conjugacy classes — view the full character table.
| maximal subgroup of | #14648275, #14648278, #14648280, … |
| maximal normal subgroup of | #14648275, #14648278, #14648280, … |
| maximal quotient of | #14752485, #14752533, #14752746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13577);