Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| isoclinism | isoclinic class of #90695 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#90696 |
| Hall | C32×C19 ⋊ D4 |
| Sylow | C19 ⋊ C3×#67 |
| Sylow | C32 ⋊ D76 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D19 |
| commutator, cosocle | C2×C3×C19 | C22×C3 |
| Frattini | C2 | C3×D3×D19 |
| Fitting, socle | C2×C32×C19 | C22 |
| hypocenter | C3×C19 | C3×D4 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C2×C3 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72277076, C3×#67×D19 |
| maximal normal subgroup of | #72277076, C3×#67×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 105);