Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #1658⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#1658⋊C3 |
| unambiguous semidirect product | #1658⋊C32 |
| unambiguous semidirect product | (C3×#1658)⋊C3 |
| Fitting | C3×#1658 ⋊ C3 |
| derived | #564 ⋊ C2×C32 |
| Sylow | #1658 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1658⋊C3 |
| commutator, cosocle, hypocenter | #564 | C2×C32 |
| Frattini | C42 | C2×C3×A4 |
| Fitting | C3×#1658 | C3 |
| socle | C22×C3 | #120⋊C3 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C3 | |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153339);