Finite Group DatabasebetaFinite Group Databasebeta| order | 2646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32×C7 |
| direct product | C2×C32⋊#3862 |
| Fitting | C2×C32×C72 ⋊ C3 |
| Hall | C2×C72 ⋊ H(3,𝔽3) |
| Sylow | C72 ⋊ C2×H(3,𝔽3) |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 126 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72224636, C2×#72224658, C2×#72224664, … |
| maximal normal subgroup of | C2×#72224636, C2×#72224658, C2×#72224664, … |
Past the SmallGroups library coverage — no SmallGroups id.