Finite Group DatabasebetaFinite Group Databasebeta| order | 7816 |
| automorphism | Aut(G) order 7628416 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3908 |
| unambiguous semidirect product | C4⋊D977 |
| Fitting | C4×C977 ⋊ C2 |
| Sylow | C977 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D977 |
| commutator, socle | C2×C977 | C22 |
| Fitting | C4×C977 | C2 |
| hypercenter | C4 | D977 |
| hypocenter | C977 | D4 |
| LCS | G ▷ C2×C977 ▷ C977 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,977|b^a=bc,d^a=d^976,d^b=d^9761957 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30627592, D7816, #30627594, … |
| maximal normal subgroup of | #30627592, D7816, #30627594, … |
| maximal quotient of | #30627584, C4⋊Dic977, D7816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7816, 10);