Finite Group DatabasebetaFinite Group Databasebeta| order | 8696 |
| automorphism | Aut(G) order 9443856 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4348 |
| unambiguous semidirect product | C4⋊D1087 |
| Fitting | C4×C1087 ⋊ C2 |
| Sylow | C1087 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1087 |
| commutator, socle | C2×C1087 | C22 |
| Fitting | C4×C1087 | C2 |
| hypercenter | C4 | D1087 |
| hypocenter | C1087 | D4 |
| LCS | G ▷ C2×C1087 ▷ C1087 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1087|b^a=bc,d^a=d^1086,d^b=d^10862177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31775018, D8696, #31775020, … |
| maximal normal subgroup of | #31775018, D8696, #31775020, … |
| maximal quotient of | (C2×D1087)⋊C4, C4⋊Dic1087, D8696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8696, 10);