Finite Group DatabasebetaFinite Group Databasebeta| order | 4684 |
| automorphism | Aut(G) order 2740140 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2342 |
| direct product | C2×D1171 |
| unambiguous semidirect product | C1171⋊C22 |
| unambiguous semidirect product | (C2×C1171)⋊C2 |
| Fitting, socle | C2×C1171 ⋊ C2 |
| derived, Sylow | C1171 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1171 |
| commutator, cosocle, hypocenter | C1171 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1171 | C2 |
| LCS | G ▷ C1171 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2342 |
1174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D1171⋊C3, D3×D1171, C2×D3513, … |
| maximal normal subgroup of | C2×D1171⋊C3, C2×C3×D1171, C2×D1171⋊C5, … |
| maximal quotient of | D3×D1171, C2×D3513, C2×C3×D1171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4684, 3);