Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#72210382 |
| Fitting, socle | C35 ⋊ C2×GL(2,𝔽3) |
| derived | #14519481 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #72210382 |
| commutator, cosocle, hypocenter | #14519481 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C2×GL(2,𝔽3) |
| LCS | G ▷ #14519481 | |
| UCS | C1 ◁ C3 | |
1661 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 1661 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
99 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210382 |
| maximal normal subgroup of | D3×#72210382 |
Past the SmallGroups library coverage — no SmallGroups id.