Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
| direct product | C3×#68006 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C16 | S4 |
| commutator, hypocenter | SL(2,𝔽3) | C3×C16 |
| Frattini | C16 | C3×S4 |
| Fitting | C3×#504 | D3 |
| socle | C2×C3 | A4⋊C16 |
| prime radical | C3×#41⋊C3 | C8 |
| cosocle | #504⋊C3 | C2×C3 |
| LCS | G ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C3×C16 | |
81 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11711660 |
| maximal normal subgroup of | C3×#11711660 |
| maximal quotient of | C3×SL(2,𝔽3)⋊C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154138);