Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#13049546 |
| derived, Sylow | C34 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #10620215 |
| commutator, hypocenter | C34 | C23×C4 |
| Frattini | C2 | C2×#10620215 |
| Fitting, socle | C22×C34 | C23 |
| prime radical | C22×C3⋊D32 | C2 |
| cosocle | C2×C34 | C24 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C22 | |
3642 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 3642 conjugacy classes of subgroups — too many to draw. Only its 315 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, C2×#72219715, #72220333, … |
| maximal normal subgroup of | C2×#72219714, C2×#72219715, #72220333, … |
Past the SmallGroups library coverage — no SmallGroups id.