Finite Group DatabasebetaFinite Group Databasebeta| order | 12288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C25 |
| direct product | C2×#72210665 |
| Fitting | C2×#72209716 ⋊ D3 |
| derived | #72210409 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72210665 |
| commutator, cosocle, hypocenter | #72210409 | C22 |
| Frattini | C26 | C2×#1020 |
| Fitting | C2×#72209716 | D3 |
| socle | C23 | #72209884 |
| LCS | G ▷ #72210409 | |
| UCS | C1 ◁ C2 | |
Only the 31 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 31 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
88 conjugacy classes — view the full character table.
| automorphism group of | #376, #379 |
Past the SmallGroups library coverage — no SmallGroups id.