Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#11710337 |
| Fitting, Sylow | C23×B(4,𝔽2) ⋊ C3 |
| derived | C22×H(5,𝔽2) ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #85645 |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C22×C3 |
| Frattini | C23 | C22×C22⋊A4 |
| Fitting | C23×B(4,𝔽2) | C3 |
| socle | C24 | #120⋊C3 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
11330 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 11330 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209719, C2×#72209660, #72311976, … |
| maximal normal subgroup of | C2×#72209719, C2×#72209660, #72311976, … |
| maximal quotient of | C2×#72210822, C2×#72212285, #72267338, … |
Past the SmallGroups library coverage — no SmallGroups id.