Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| isoclinism | isoclinic class of #92694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#92694 |
| Hall | C32×C72 ⋊ D4 |
| Sylow | C72 ⋊ #626 |
| Sylow | C32 ⋊ C7×C22⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | (C3⋊D3)⋊D7 |
| commutator, cosocle | C2×C32×C7 | C22×C7 |
| Frattini | C2 | C7×(C3⋊D3)⋊D7 |
| Fitting, socle | C2×C32×C72 | C22 |
| hypocenter | C32×C7 | C7×D4 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2×C7 | |
238 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
357 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72222162, C7×#11759644, #72222235, … |
| maximal normal subgroup of | #72222162, C7×#11759644, #72222235, … |
Past the SmallGroups library coverage — no SmallGroups id.