Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×#87704 |
| unambiguous semidirect product | C3⋊(C22×#87704) |
| unambiguous semidirect product | (C2×C3)⋊(C2×#87704) |
| Fitting, socle | C2×C3×C7×C19 ⋊ C2×C3 |
| derived | C3×C7×C19 ⋊ C22×C3 |
| Hall | C3×#87704 ⋊ C22 |
| Hall | C7×C19 ⋊ C2×C3×D3 |
| Sylow | C19 ⋊ C2×D3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×D3×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×#87704 |
| commutator, cosocle, hypocenter | C3×C7×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C19 | C2×C3 |
| LCS | G ▷ C3×C7×C19 | |
| UCS | C1 ◁ C2 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D5×#87704, C2×C5×D3×#87704, C2×D15×#87704, … |
| maximal normal subgroup of | C2×C5×D3×#87704, C2×D3×C7×#87704 |
| maximal quotient of | D3×D5×#87704, C2×C5×D3×#87704, C2×D15×#87704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 208);