Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#72230842 |
| Fitting | C23×C3×H(5,𝔽2) ⋊ D3 |
| derived | C3×C22⋊#997 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊#87588 |
| commutator, cosocle, hypocenter | C3×C22⋊#997 | C22 |
| Frattini | C2 | C2×C3⋊#87588 |
| Fitting | C23×C3×H(5,𝔽2) | D3 |
| socle | C24×C3 | #1020 |
| LCS | G ▷ C3×C22⋊#997 | |
| UCS | C1 ◁ C22 | |
19092 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 19092 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11715850, C2×#72231618, C2×#72231672 |
| maximal normal subgroup of | C2×D3×#11715850, C2×#72231618, C2×#72231672 |
| maximal quotient of | C2×#72230852 |
Past the SmallGroups library coverage — no SmallGroups id.