Finite Group DatabasebetaFinite Group Databasebeta| order | 3318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D553 |
| Fitting, socle, Hall | C3×C7×C79 ⋊ C2 |
| derived, Hall | C7×C79 ⋊ C2×C3 |
| Hall | C3×C79 ⋊ D7 |
| Sylow | C79 ⋊ C3×D7 |
| Hall | C3×C7 ⋊ D79 |
| Sylow | C7 ⋊ C3×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D553 |
| commutator, cosocle, hypocenter | C7×C79 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C79 | C2 |
| LCS | G ▷ C7×C79 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1659 |
834 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D553, C3×D2765, C3×D3871, … |
| maximal normal subgroup of | C3×C5×D553, C3×C7×D553, C3×C11×D553 |
| maximal quotient of | C3×C5×D553, C3×D2765, C3×D3871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3318, 8);