Finite Group DatabasebetaFinite Group Databasebeta| order | 7864 |
| automorphism | Aut(G) order 7722448 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3932 |
| unambiguous semidirect product | C4⋊D983 |
| Fitting | C4×C983 ⋊ C2 |
| Sylow | C983 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D983 |
| commutator, socle | C2×C983 | C22 |
| Fitting | C4×C983 | C2 |
| hypercenter | C4 | D983 |
| hypocenter | C983 | D4 |
| LCS | G ▷ C2×C983 ▷ C983 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,983|b^a=bc,d^a=d^982,d^b=d^9821969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30628460, D7864, #30628462, … |
| maximal normal subgroup of | #30628460, D7864, #30628462, … |
| maximal quotient of | (C2×D983)⋊C4, C4⋊Dic983, D7864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7864, 10);