Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×#13091120 |
| Fitting, Sylow | C3×#10624749 ⋊ C2 |
| derived | #10624749 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13091120 |
| commutator, cosocle, hypocenter | #10624749 | C2×C3 |
| Frattini | C33 | C3×C3⋊(C3⋊D3) |
| Fitting | C3×#10624749 | C2 |
| socle | C32 | #92338 |
| LCS | G ▷ #10624749 | |
| UCS | C1 ◁ C3 | |
2200 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 2200 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72221925, #72221960, #72222257, … |
| maximal normal subgroup of | C32×#13091120, C2×C3×#13091120, C3×#72210336 |
| maximal quotient of | A4×#13091120, ΓL(1,𝔽8)×#13091120, C32×#13091120, … |
Past the SmallGroups library coverage — no SmallGroups id.