Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #1308⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1308⋊C3 |
| unambiguous semidirect product | #1308⋊C32 |
| unambiguous semidirect product | (C3×#1308)⋊C3 |
| Fitting | C3×#1308 ⋊ C3 |
| derived, Sylow | #1308 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1308⋊C3 |
| commutator, cosocle, hypocenter | #1308 | C32 |
| Frattini | C2×C42 | C3×A4 |
| Fitting | C3×#1308 | C3 |
| socle | C22×C3 | #95⋊C3 |
| LCS | G ▷ #1308 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153317);