Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×#6053 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | D3×#6053 |
| Fitting, socle, derived, Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ D3×C8 |
| Sylow | C3 ⋊ C2×#6053 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52 | C2×C8 |
| prime radical | D3×C5⋊D5 | C4 |
| cosocle | C3×#1043 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 | |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30 |
33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6053⋊C2, D3×AGL(1,𝔽25), D3×#10597167 |
| maximal normal subgroup of | D3×#6053⋊C2, D3×AGL(1,𝔽25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 955);