Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C22×#72217027 |
| Fitting | C22×#60399 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C26 |
| Frattini | C23 | C25×S4 |
| Fitting | C22×#60399 | D3 |
| hypercenter | C22×D4 | #1020⋊C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
At least 9757 conjugacy classes of subgroups; only the 3651 normal subgroups are shown.
248 conjugacy classes — view the full character table.
| maximal quotient of | C2×#72247039 |
Past the SmallGroups library coverage — no SmallGroups id.