Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#13090904 |
| Fitting | C2×#10624688 ⋊ C2 |
| Sylow | #10624688 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C22×C32 |
| Frattini | C33 | C2×C32×D3 |
| Fitting | C2×#10624688 | C2 |
| socle | C2×C32 | C3×(C3⋊D3)⋊C3 |
| prime radical | C2×#92174 | C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C2×C9 | |
493 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 493 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72277433 |
Past the SmallGroups library coverage — no SmallGroups id.