Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#72241282 |
| Fitting, Sylow | C2×#7629120 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #85645 |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C23×C3 |
| Frattini | C23 | C23×C22⋊A4 |
| Fitting | C2×#7629120 | C3 |
| socle | C24 | C22×C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C2×C4 | |
100808 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 100808 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
128 conjugacy classes — view the full character table.
| maximal quotient of | C2×C4×#35346⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.