Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | D4×#92314 |
| Fitting | D4×#6900 ⋊ C2 |
| Sylow | #6900 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×#92314 |
| commutator, cosocle | C2×C92 | C23×C3 |
| Frattini, socle | C2×C32 | C22×C3×C3⋊D3 |
| Fitting | D4×#6900 | C2 |
| hypercenter | D4 | #92314 |
| hypocenter | C92 | C2×C3×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2 ◁ D4 | |
1338 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1338 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×#92314, #72219903, #72219918, … |
| maximal normal subgroup of | C2×D4×#92314, #72219903, #72219918, … |
| maximal quotient of | C2×D4×#92314, #72219949, #72220018, … |
Past the SmallGroups library coverage — no SmallGroups id.