Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×D3×C22⋊A4 |
| Fitting, socle | C27×C3 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C24×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×C22⋊A4 |
| commutator, cosocle, hypocenter | C24×C3 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C27×C3 | C2×C3 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C23 | |
279808 conjugacy classes of subgroups; only the 664 normal subgroups are shown.
This group has 279808 conjugacy classes of subgroups — too many to draw. Only its 664 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D3×#1020, C2×D3×#11710730, C2×D3×#35346⋊C3, … |
| maximal normal subgroup of | C23×D3×#1020, C2×D3×AΣL(1,𝔽64), C2×D3×#87524 |
Past the SmallGroups library coverage — no SmallGroups id.