Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C7 |
| direct product | C2×#41×C7⋊D7 |
| Fitting | C2×C72×#41 ⋊ C2 |
| Sylow | C72 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×C7⋊D7 |
| commutator, cosocle | C2×C72 | C25 |
| Frattini | C2 | C24×C7⋊D7 |
| Fitting | C2×C72×#41 | C2 |
| socle | C22×C72 | C24 |
| hypercenter | C2×#41 | C7⋊D7 |
| hypocenter | C72 | C22×#41 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
4450 conjugacy classes of subgroups; only the 1015 normal subgroups are shown.
This group has 4450 conjugacy classes of subgroups — too many to draw. Only its 1015 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 784 |
520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×AGL(1,ℤ/8)×C7⋊D7, C2×#41×#64424 |
| maximal normal subgroup of | C2×AGL(1,ℤ/8)×C7⋊D7, C2×#41×#64424 |
Past the SmallGroups library coverage — no SmallGroups id.