Finite Group DatabasebetaFinite Group Databasebeta| order | 11864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D1483 |
| Fitting | C22×C1483 ⋊ C2 |
| Sylow | C1483 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1483 |
| commutator, socle, cosocle | C2×C1483 | C22 |
| Fitting | C22×C1483 | C2 |
| hypercenter | C22 | D1483 |
| hypocenter | C1483 | D4 |
| LCS | G ▷ C2×C1483 ▷ C1483 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1483|b^a=bc,d^b=d^14822969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D1483, C2×C22⋊D1483, #37557520, … |
| maximal normal subgroup of | D4×D1483, C2×C22⋊D1483, #37557520, … |
| maximal quotient of | (C2×D1483)⋊C4, C22⋊Dic1483, Dic1483⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11864, 9);