Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C28 |
| direct product | #120×C22⋊A4 |
| Fitting, Sylow | C24×#120 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C22⋊A4 |
| commutator, socle, cosocle | C26 | C23×C3 |
| Fitting | C24×#120 | C3 |
| hypercenter | #120 | C22⋊A4 |
| hypocenter | C24 | C3×#120 |
| LCS | G ▷ C26 ▷ C24 | |
| UCS | C1 ◁ C22 ◁ #120 | |
94695 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 94695 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
112 conjugacy classes — view the full character table.
| maximal subgroup of | #120×#1020, #72222909, C22⋊A4×#1020, … |
| maximal normal subgroup of | #120×#1020, #72220576, #72222909, … |
| maximal quotient of | #72247549 |
Past the SmallGroups library coverage — no SmallGroups id.