Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72220635 |
| Fitting, socle | C2×C32×C13 ⋊ C2×C3×C4 |
| derived | C32×C13 ⋊ C22×C3×C4 |
| Hall | C32×C13⋊C3 ⋊ C22×C4 |
| Sylow | C13 ⋊ C2×C3×#624 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72220635 |
| commutator, hypocenter | C32×C13 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C13 | C2×C3×C4 |
| prime radical | C2×C3⋊D3×D13⋊C3 | C2 |
| cosocle | C32×D13 | C23×C3 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C2 | |
580 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #624×AGL(1,𝔽13), C2×D32×AGL(1,𝔽13), #72242000, … |
| maximal normal subgroup of | #624×AGL(1,𝔽13), C2×D32×AGL(1,𝔽13), #72242000, … |
| maximal quotient of | #72242005 |
Past the SmallGroups library coverage — no SmallGroups id.