Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #85645 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C3×#85645 |
| Fitting | C22×C3×#120 ⋊ C3 |
| derived | C26 ⋊ C2×C32 |
| Sylow | C22×#120 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #85645 |
| commutator, cosocle, hypocenter | C26 | C2×C32 |
| Frattini | C22 | C2×C3×C22⋊A4 |
| Fitting | C22×C3×#120 | C3 |
| socle | C24×C3 | C2×A4 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C3 | |
1728 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#85645, C3×#87588⋊C2, #72231670, … |
| maximal normal subgroup of | D3×#85645, C3×#87588⋊C2, #72231670, … |
| maximal quotient of | C3×#35346⋊C3, C2×C3×#85645 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153827);