Finite Group DatabasebetaFinite Group Databasebeta| order | 7892 |
| automorphism | Aut(G) order 7781512 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3946 |
| direct product | C2×D1973 |
| unambiguous semidirect product | C1973⋊C22 |
| unambiguous semidirect product | (C2×C1973)⋊C2 |
| Fitting, socle | C2×C1973 ⋊ C2 |
| derived, Sylow | C1973 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1973 |
| commutator, hypocenter | C1973 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1973 | C2 |
| LCS | G ▷ C1973 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
1976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1973, C22⋊D1973, D7892, … |
| maximal normal subgroup of | C4×D1973, C22⋊D1973, D7892, … |
| maximal quotient of | C4×D1973, C2×Dic1973, C22⋊D1973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7892, 4);