Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | #157×#626 |
| Sylow | C34 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×#157 |
| commutator, Fitting, socle | C2×C34 | C22×C4 |
| prime radical | C3⋊D3×#626 | C2 |
| cosocle | C2×C32×C3⋊D3 | C23 |
| hypocenter | C34 | C4×D4 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
876 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #626×PSU(3,𝔽2) |
| maximal normal subgroup of | #626×PSU(3,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.