Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C8×#92314 |
| Fitting | C8×#6900 ⋊ C2 |
| derived | C92 ⋊ C2×C3×C8 |
| Sylow | #6900 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #92314 |
| commutator, hypocenter | C92 | C2×C3×C8 |
| Frattini | C32×C4 | C2×C3×C3⋊D3 |
| Fitting | C8×#6900 | C2 |
| socle | C2×C32 | C3×C4×C3⋊D3 |
| prime radical | C2×#92314 | C4 |
| cosocle | C4×C92 | C22×C3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C8 | |
554 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C8×#92314, M16×#92314, SD16×#92314, … |
| maximal normal subgroup of | C2×C8×#92314, M16×#92314, SD16×#92314, … |
| maximal quotient of | C2×C8×#92314 |
Past the SmallGroups library coverage — no SmallGroups id.