Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of #6057⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C2×#6057⋊C3 |
| unambiguous semidirect product | (C2×#6057)⋊C3 |
| Fitting, socle | C2×C52 ⋊ SL(2,𝔽3) |
| derived | #6057 ⋊ C2×C3 |
| Hall | C2×#6057 ⋊ C3 |
| Sylow | C52 ⋊ C2×SL(2,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #6057⋊C3 |
| commutator, cosocle, hypocenter | #6057 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52 | SL(2,𝔽3) |
| LCS | G ▷ #6057 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 50 |
16 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 950);