Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#92184⋊C3 |
| Fitting | C2×#10624704 ⋊ C2 |
| derived | C3×C27 ⋊ C22×C32 |
| Sylow | #10624704 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92184⋊C3 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C32 |
| Frattini | C3×C9 | C2×C32×D3 |
| Fitting | C2×#10624704 | C2 |
| socle | C2×C3 | C3×#4169 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2 | |
364 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221837, C2×#72221840, C2×#72221843, … |
| maximal normal subgroup of | C2×#72221837, C2×#72221840, C2×#72221843, … |
Past the SmallGroups library coverage — no SmallGroups id.