Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C26 |
| direct product | C2×#11715851 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #87588 |
| commutator, cosocle, hypocenter | C22⋊#997 | C22 |
| Frattini | C2 | C2×#87588 |
| Fitting | C23×H(5,𝔽2) | D3 |
| socle | C24 | #1020 |
| prime radical | C2×C22⋊#997 | C2 |
| LCS | G ▷ C22⋊#997 | |
| UCS | C1 ◁ C22 | |
7928 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 7928 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210040, C2×#72215537, C2×#72233583, … |
| maximal normal subgroup of | C2×#72215537, C2×#72233583, #72267095, … |
| maximal quotient of | C2×#72219111, C2×#72209782 |
Past the SmallGroups library coverage — no SmallGroups id.