Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#72221927 |
| Fitting | C2×H(5,𝔽3) ⋊ GL(2,𝔽3) |
| derived | #72209952 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #72210299 |
| commutator, cosocle, hypocenter | #72209952 | C22 |
| Frattini | C3 | C2×#72210299 |
| Fitting | C2×H(5,𝔽3) | GL(2,𝔽3) |
| LCS | G ▷ #72209952 | |
| UCS | C1 ◁ C2×C3 | |
1373 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 1373 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
74 conjugacy classes — view the full character table.
| automorphism group of | C32×C9, C2×C32×C9 |
| outer automorphism group of | C32×C9, C2×C32×C9 |
Past the SmallGroups library coverage — no SmallGroups id.