Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C34 |
| direct product | C2×#13091042 |
| Fitting | C2×#10624731 ⋊ C2 |
| derived | C33×C9 ⋊ C22×C3 |
| Sylow | #10624731 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13091042 |
| commutator, cosocle, hypocenter | C33×C9 | C22×C3 |
| Frattini | C33 | C2×C3×C3⋊D3 |
| Fitting | C2×#10624731 | C2 |
| socle | C2×C32 | C3⋊((C3⋊D3)⋊C3) |
| LCS | G ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
1048 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221903, C2×#72221908 |
| maximal normal subgroup of | C2×#72221903, C2×#72221908 |
Past the SmallGroups library coverage — no SmallGroups id.