Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#72213199 |
| Fitting, socle | C2×C34 ⋊ C4×C8 |
| derived, Sylow | C34 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213199 |
| commutator, hypocenter | C34 | C2×C4×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C4×C8 |
| prime radical | C2×C3⋊D32 | C2×C4 |
| cosocle | #10620198 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
558 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213315, #72220584, #72220811, … |
| maximal normal subgroup of | C2×#72213315, #72220584, #72220811, … |
| maximal quotient of | #72220269, #72220584, D3×#72213199, … |
Past the SmallGroups library coverage — no SmallGroups id.