Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×#13091158 |
| Fitting | C2×#10624761 ⋊ C2 |
| derived | C34 ⋊ C22×C32 |
| Sylow | #10624761 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13091158 |
| commutator, cosocle, hypocenter | C34 | C22×C32 |
| Frattini | C33 | C2×C32×D3 |
| Fitting | C2×#10624761 | C2 |
| socle | C2×C3 | #92258 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C2 | |
574 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221885, C2×#72221895 |
| maximal normal subgroup of | C2×#72221895 |
Past the SmallGroups library coverage — no SmallGroups id.