Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C29 |
| direct product | C2×#11710913 |
| Fitting, Sylow | C25×#41 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C24×Q8 | C22×C3 |
| Frattini | C2 | C22×C22⋊(C22⋊A4) |
| Fitting | C25×#41 | C3 |
| socle | C26 | C2×A4 |
| LCS | G ▷ C24×Q8 | |
| UCS | C1 ◁ C2×C4 | |
152253 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 152253 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72210817, C2×#72211558, C2×#72211543, … |
| maximal normal subgroup of | C2×#72210817, C2×#72211558, C2×#72211543, … |
Past the SmallGroups library coverage — no SmallGroups id.