Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2933 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D11 |
| commutator, socle | C22×C11 | C23×C4 |
| Fitting, prime radical | C11×#525 | C2 |
| cosocle | C2×C4×C11 | C24 |
| hypercenter | #525 | D11 |
| hypocenter | C11 | #2933 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,f^2=g,b^a=be,h^a=h^10,d^c=dg,h^c=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14774507, #14774514, #14774522, … |
| maximal normal subgroup of | #14774507, #14774514, #14774522, … |
| maximal quotient of | #14724661, #14724672, #14724685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13237);