Finite Group DatabasebetaFinite Group Databasebeta| order | 2808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#64603⋊C3 |
| Hall | C32×C13⋊C3 ⋊ D4 |
| Sylow | C13 ⋊ C32×#67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×D13⋊C3 |
| commutator, cosocle | C2×C3×C13 | C22×C32 |
| Frattini | C2 | C3×D3×D13⋊C3 |
| Fitting, socle | C2×C32×C13 | C22×C3 |
| hypocenter | C3×C13 | C32×D4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2×C3 | |
272 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#67×D13⋊C3, #72241988, #72241989 |
| maximal normal subgroup of | C3×#67×D13⋊C3, #72241988, #72241989 |
Past the SmallGroups library coverage — no SmallGroups id.