Finite Group DatabasebetaFinite Group Databasebeta| order | 5616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | #626×D13⋊C3 |
| Hall | C32×C13⋊C3 ⋊ C2×D4 |
| Sylow | C13 ⋊ C2×C3×#626 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×D13⋊C3 |
| commutator, Fitting, socle, cosocle | C2×C32×C13 | C23×C3 |
| hypocenter | C32×C13 | C2×C3×D4 |
| LCS | G ▷ C2×C32×C13 ▷ C32×C13 | |
| UCS | C1 ◁ C2 | |
612 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 94 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 | D13⋊C3×#3811, #626×AGL(1,𝔽13), #72242017 |
| maximal normal subgroup of | D13⋊C3×#3811, #626×AGL(1,𝔽13), #72242017 |
Past the SmallGroups library coverage — no SmallGroups id.