Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#72231199 |
| Fitting | C24×#95 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#85547 |
| commutator, cosocle, hypocenter | C22⋊(#95⋊C3) | C23 |
| Frattini | C23 | C22×#1020 |
| Fitting | C24×#95 | D3 |
| socle | C26 | C2×S4 |
| hypercenter | C23 | #85547 |
| LCS | G ▷ C22⋊(#95⋊C3) | |
| UCS | C1 ◁ C22 ◁ C23 | |
18820 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 18820 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72260440 |
| maximal normal subgroup of | #72260440 |
Past the SmallGroups library coverage — no SmallGroups id.