Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊(#120⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C22×C3⋊(#120⋊C3) |
| Fitting | C26×C3 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(#120⋊C3) |
| commutator, cosocle, hypocenter | C24×C3 | C23×C3 |
| Frattini | C22 | C22×D3×A4 |
| Fitting | C26×C3 | C2×C3 |
| socle | C24×C3 | C2×A4 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C22 | |
1743 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 1743 conjugacy classes of subgroups — too many to draw. Only its 73 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 | C22×#10593244, C2×#72230753, C22×D3×#120⋊C3, … |
| maximal normal subgroup of | C22×#10593244, C22×D3×#120⋊C3, C2×#73861⋊C3, … |
| maximal quotient of | #72274889, C2×#84128⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157421);