Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D34 |
| Fitting, socle | C2×C34 ⋊ C24 |
| derived, Sylow | C34 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D34 |
| commutator, cosocle, hypocenter | C34 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | C24 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
7941 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 7941 conjugacy classes of subgroups — too many to draw. Only its 760 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
162 conjugacy classes — view the full character table.
| maximal subgroup of | #72220351 |
| maximal normal subgroup of | #72220351 |
| maximal quotient of | #72220350, #72220351 |
Past the SmallGroups library coverage — no SmallGroups id.