Finite Group DatabasebetaFinite Group Databasebeta| order | 7432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D929 |
| Fitting | C22×C929 ⋊ C2 |
| Sylow | C929 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D929 |
| commutator, socle | C2×C929 | C22 |
| Fitting | C22×C929 | C2 |
| hypercenter | C22 | D929 |
| hypocenter | C929 | D4 |
| LCS | G ▷ C2×C929 ▷ C929 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,929|b^a=bc,d^b=d^9281861 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D929, C2×C22⋊D929, #28415449, … |
| maximal normal subgroup of | D4×D929, C2×C22⋊D929, #28415449, … |
| maximal quotient of | #28415427, C22⋊Dic929, #28415429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7432, 9);