Finite Group DatabasebetaFinite Group Databasebeta| order | 6144 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×D4×#73026 |
| Fitting | C2×D4×B(4,𝔽2) ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#1020⋊C2 |
| commutator, cosocle | C2×#997 | C25 |
| Frattini | C24 | C24×S4 |
| Fitting | C2×D4×B(4,𝔽2) | D3 |
| hypercenter | C22×D4 | #1020⋊C2 |
| hypocenter | #997 | C23×D4 |
| LCS | G ▷ C2×#997 ▷ #997 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
At least 10657 conjugacy classes of subgroups; only the 659 normal subgroups are shown.
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72247039 |
| maximal normal subgroup of | C2×#72247039 |
Past the SmallGroups library coverage — no SmallGroups id.