Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C16 · Schur multiplier (H2) = C3 |
| direct product | C3×#2258⋊C3 |
| unambiguous semidirect product | #2258⋊C32 |
| unambiguous semidirect product | (C3×#2258)⋊C3 |
| Fitting | C3×#2258 ⋊ C3 |
| Sylow | #2258 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C32 | A4 |
| commutator, hypocenter | Q8 | C32×C16 |
| Frattini | C16 | C2×C3×A4 |
| Fitting | C3×#2258 | C3 |
| socle | C2×C3 | A4×C16 |
| prime radical | C3×#41⋊C3 | C8 |
| cosocle | #504 | C2×C32 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C3×C32 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
336 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13737⋊C3, C3×#11711660 |
| maximal normal subgroup of | C3×#13737⋊C3, C3×#11711660 |
| maximal quotient of | C3×SL(2,𝔽3)×C32 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153395);