Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#72991 |
| Fitting | C3×#379 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1020⋊C2 |
| commutator, cosocle | C2×C22⋊A4 | C22×C3 |
| Frattini | C23 | C2×C3×S4 |
| Fitting | C3×#379 | D3 |
| socle | C23×C3 | C2×S4 |
| hypocenter | C22⋊A4 | C3×D4 |
| LCS | G ▷ C2×C22⋊A4 ▷ C22⋊A4 | |
| UCS | C1 ◁ C2×C3 | |
559 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 559 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11713200, #72229187, D3×#72991, … |
| maximal normal subgroup of | C3×#11713200, #72229187, D3×#72991, … |
| maximal quotient of | C2×C3×#72991, C3×#72215885 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154780);