Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C22×#11715753 |
| Fitting | C22×#3532 ⋊ D3 |
| derived | #5464 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #11715753 |
| commutator, cosocle, hypocenter | #5464 | C24 |
| Frattini | C22 | C23×#1020 |
| Fitting | C22×#3532 | D3 |
| socle | C24 | C2×#1020 |
| LCS | G ▷ #5464 | |
| UCS | C1 ◁ C22 | |
27109 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 27109 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72218857, C2×#72341130, C2×#72341141 |
| maximal normal subgroup of | C22×#72218857, C2×#72341130, C2×#72341141 |
| maximal quotient of | C2×#72240895, C2×#72341130 |
Past the SmallGroups library coverage — no SmallGroups id.