Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#72340506 |
| Fitting, Sylow | C2×#8075294 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #63011⋊C3 |
| commutator, cosocle | C2×H(3,𝔽4) | C23×C3 |
| Frattini | C23 | C23×C22⋊A4 |
| Fitting | C2×#8075294 | C3 |
| socle | C24 | C22×C22⋊A4 |
| hypocenter | H(3,𝔽4) | C2×C3×D4 |
| LCS | G ▷ C2×H(3,𝔽4) ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C22 | |
29523 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 29523 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72340508, C2×#72341141 |
| maximal normal subgroup of | C2×#72340508, C2×#72341141 |
Past the SmallGroups library coverage — no SmallGroups id.