Finite Group DatabasebetaFinite Group Databasebeta| order | 3456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C2×#13180056 |
| Fitting | C25×C32 ⋊ C2×D3 |
| derived | C32⋊(C22⋊A4) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13180056 |
| commutator, cosocle, hypocenter | C32⋊(C22⋊A4) | C23 |
| Frattini | C3 | C2×D3×#1020 |
| Fitting | C25×C32 | C2×D3 |
| socle | C25×C3 | D32 |
| LCS | G ▷ C32⋊(C22⋊A4) | |
| UCS | C1 ◁ C2 | |
6607 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 6607 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213328 |
Past the SmallGroups library coverage — no SmallGroups id.