Finite Group DatabasebetaFinite Group Databasebeta| order | 11728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C733 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D733 |
| commutator | C2×C733 | C2×C4 |
| Fitting | C2×C4×C733 | C2 |
| socle, prime radical, cosocle | C22×C733 | C22 |
| hypercenter | C2×C4 | D733 |
| hypocenter | C733 | C4⋊C4 |
| LCS | G ▷ C2×C733 ▷ C733 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,733|a^2=d,b^2=c,b^a=bc,e^b=e^7322938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C4×D733, C2×#26043992, #37553130, … |
| maximal normal subgroup of | C4⋊C4×D733, C2×#26043992, #37553130, … |
| maximal quotient of | #37553081, #37553103, #37553105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11728, 19);