Finite Group DatabasebetaFinite Group Databasebeta| order | 11888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic743⋊C4 |
| Sylow | C743 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D743 |
| commutator | C2×C743 | C2×C4 |
| Fitting | C2×C4×C743 | C2 |
| socle, prime radical, cosocle | C22×C743 | C22 |
| hypercenter | C2×C4 | D743 |
| hypocenter | C743 | C4⋊C4 |
| LCS | G ▷ C2×C743 ▷ C743 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,743|a^2=d,b^2=c,b^a=bc,e^b=e^7422978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C4×D743, C2×Dic743⋊C4, #37557935, … |
| maximal normal subgroup of | C4⋊C4×D743, C2×Dic743⋊C4, #37557935, … |
| maximal quotient of | C743⋊#95, Dic743⋊C8, #37557910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11888, 19);