Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#13049813 |
| Fitting, socle | C22×C34 ⋊ C2×D4 |
| Sylow | C34 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #13049813 |
| commutator, cosocle | C3⋊(C3⋊(C3⋊D3)) | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C2×D4 |
| hypocenter | C34 | C23×D4 |
| LCS | G ▷ C3⋊(C3⋊(C3⋊D3)) ▷ C34 | |
| UCS | C1 ◁ C22 | |
9136 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 9136 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
144 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72210346, #72220744, #72220834, … |
| maximal normal subgroup of | C22×#72210346, #72220744, #72220834, … |
| maximal quotient of | C22×#72219698 |
Past the SmallGroups library coverage — no SmallGroups id.