Finite Group DatabasebetaFinite Group Databasebeta| order | 8748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#72214331 |
| Fitting, Sylow | C3×H(3,𝔽3)2 ⋊ C22 |
| derived | H(3,𝔽3)2 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #72214331 |
| commutator, cosocle, hypocenter | H(3,𝔽3)2 | C22×C3 |
| Frattini | C32 | C3×C3⋊D32 |
| Fitting | C3×H(3,𝔽3)2 | C22 |
| socle | C33 | C3⋊D32 |
| LCS | G ▷ H(3,𝔽3)2 | |
| UCS | C1 ◁ C3 | |
6828 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 6828 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72214399 |
| maximal normal subgroup of | C3×#72214399 |
| maximal quotient of | #72222000, #72222003, #72243793, … |
Past the SmallGroups library coverage — no SmallGroups id.