Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×#72240986 |
| Fitting | C2×#6372744 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#11713272 |
| commutator, cosocle | #5950 | C25 |
| Frattini | C22×C4 | C24×S4 |
| Fitting | C2×#6372744 | D3 |
| hypercenter | C2×M16 | #1020⋊C2 |
| hypocenter | #997 | C23×D4 |
| LCS | G ▷ #5950 ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×M16 | |
At least 14543 conjugacy classes of subgroups; only the 691 normal subgroups are shown.
164 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.