Finite Group DatabasebetaFinite Group Databasebeta| order | 4788 |
| automorphism | Aut(G) order 1551312 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2394 |
| direct product | C2×D1197 |
| unambiguous semidirect product | (C2×C7)⋊D171 |
| unambiguous semidirect product | (C2×C9)⋊D133 |
| unambiguous semidirect product | (C2×C19)⋊D63 |
| Fitting | C2×C7×C9×C19 ⋊ C2 |
| derived, Hall | C7×C9×C19 ⋊ C22 |
| Hall | C9×C19 ⋊ C2×D7 |
| Hall | C7×C19 ⋊ C2×D9 |
| Hall | C7×C9 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D63 |
| Sylow | C9 ⋊ C2×D133 |
| Sylow | C7 ⋊ C2×D171 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1197 |
| commutator, cosocle, hypocenter | C7×C9×C19 | C22 |
| Frattini | C3 | C2×D399 |
| Fitting | C2×C7×C9×C19 | C2 |
| socle | C2×C3×C7×C19 | D3 |
| LCS | G ▷ C7×C9×C19 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
1200 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1197, C2×D5985, C2×C5×D1197, … |
| maximal normal subgroup of | C2×C5×D1197, C2×C7×D1197, D4788 |
| maximal quotient of | D5×D1197, C2×D5985, C2×C5×D1197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4788, 64);