Finite Group DatabasebetaFinite Group Databasebeta| order | 2916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×#13091105 |
| Fitting | C2×UT(4,𝔽3) ⋊ C2 |
| derived | H(5,𝔽3) ⋊ C22×C3 |
| Sylow | UT(4,𝔽3) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #92301 |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C22×C3 |
| Frattini | C33 | C2×C3×C3⋊D3 |
| Fitting | C2×UT(4,𝔽3) | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
1000 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209952, C2×#72210398, C2×#72212528, … |
| maximal normal subgroup of | C2×#72210398, C2×#72212528, C2×#72212539, … |
| maximal quotient of | C2×C3×#13091105 |
Past the SmallGroups library coverage — no SmallGroups id.