Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C32 |
| direct product | C2×#72213277 |
| Fitting, socle | C2×C34 ⋊ C4⋊Q8 |
| Sylow | C34 ⋊ C2×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213277 |
| commutator, cosocle | C3⋊D32 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C4⋊Q8 |
| prime radical | C2×C3⋊D32 | C23 |
| hypocenter | C34 | C2×C4⋊Q8 |
| LCS | G ▷ C3⋊D32 ▷ C34 | |
| UCS | C1 ◁ C2 | |
868 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213315, #72220785, #72220805, … |
| maximal normal subgroup of | C2×#72213315, #72220785, #72220805, … |
| maximal quotient of | #72220296, #72220785, C22×#72213277 |
Past the SmallGroups library coverage — no SmallGroups id.