Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#10620215 |
| Fitting, socle | C22×C34 ⋊ C23 |
| derived, Sylow | C34 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #10620215 |
| commutator, cosocle, hypocenter | C34 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | C23 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
8538 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 8538 conjugacy classes of subgroups — too many to draw. Only its 763 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72219714, C22×#13049813, #72220314, … |
| maximal normal subgroup of | C2×#72219714, C22×#13049813, #72220314, … |
| maximal quotient of | C2×#72219714, C22×#13049549 |
Past the SmallGroups library coverage — no SmallGroups id.