Finite Group DatabasebetaFinite Group Databasebeta| order | 11728 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C733 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #15668640 |
| commutator, hypocenter | C733 | C16 |
| Fitting | C4×C733 | C4 |
| socle, prime radical | C2×C733 | C8 |
| cosocle | #19154462 | C2 |
| LCS | G ▷ C733 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,733|a^2=b,b^2=c,c^2=d,e^a=e^380,e^b=e^732748 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26044016, D733⋊C16, #37553248, … |
| maximal normal subgroup of | C2×#26044016, D733⋊C16, #37553248, … |
| maximal quotient of | #37553224, C2×#26044016 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11728, 43);