Finite Group DatabasebetaFinite Group Databasebeta| order | 2178 |
| isoclinism | isoclinic class of #10624391 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#10624391 |
| Fitting, socle | C3×C112 ⋊ D3 |
| derived | C112⋊C3 ⋊ C2×C3 |
| Hall | C3×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10624391 |
| commutator, cosocle, hypocenter | C112⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 99 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2178, 21);