Finite Group DatabasebetaFinite Group Databasebeta| order | 7432 |
| automorphism | Aut(G) order 6896896 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3716 |
| unambiguous semidirect product | C4⋊D929 |
| Fitting | C4×C929 ⋊ C2 |
| Sylow | C929 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D929 |
| commutator, socle | C2×C929 | C22 |
| Fitting | C4×C929 | C2 |
| hypercenter | C4 | D929 |
| hypocenter | C929 | D4 |
| LCS | G ▷ C2×C929 ▷ C929 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,929|b^a=bc,d^a=d^928,d^b=d^9281861 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28415435, D7432, #28415437, … |
| maximal normal subgroup of | #28415435, D7432, #28415437, … |
| maximal quotient of | #28415427, C4⋊Dic929, D7432, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7432, 10);