Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#11716115 |
| Fitting | C22×C4×C72 ⋊ C22 |
| Sylow | C72 ⋊ C2×C4×D4 |
1206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽5)×#11716115, C4×#72210376 |
| maximal normal subgroup of | C4×#72210376 |
| maximal quotient of | AGL(1,𝔽5)×#11716115 |
Past the SmallGroups library coverage — no SmallGroups id.