Finite Group DatabasebetaFinite Group Databasebeta| order | 4812 |
| automorphism | Aut(G) order 1924800 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2406 |
| direct product | C2×D1203 |
| unambiguous semidirect product | (C2×C3)⋊D401 |
| unambiguous semidirect product | (C2×C401)⋊D3 |
| Fitting, socle | C2×C3×C401 ⋊ C2 |
| derived, Hall | C3×C401 ⋊ C22 |
| Sylow | C401 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D401 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1203 |
| commutator, cosocle, hypocenter | C3×C401 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C401 | C2 |
| LCS | G ▷ C3×C401 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2406 |
1206 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3609, D3×D1203, C2×C3⋊D1203, … |
| maximal normal subgroup of | C2×C3×D1203, C2×C3⋊(D401⋊C5), C2×C5×D1203, … |
| maximal quotient of | C2×D3609, D3×D1203, C2×C3⋊D1203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4812, 10);