Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×#92318⋊C3 |
| Fitting | C2×#10624918 ⋊ C2 |
| derived | C3×C27 ⋊ C22×C32 |
| Sylow | #10624918 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92318⋊C3 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C32 |
| Frattini | C9 | C2×C32×C3⋊D3 |
| Fitting | C2×#10624918 | C2 |
| socle | C2×C3 | C32×C3⋊D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2 | |
686 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72221819, C2×#72221820, C2×#72221837, … |
| maximal normal subgroup of | C2×#72221820, C2×#72221837, C2×#72221844, … |
Past the SmallGroups library coverage — no SmallGroups id.