Finite Group DatabasebetaFinite Group Databasebeta| order | 2604 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×D21 |
| unambiguous semidirect product | (C2×C3)⋊(D7×C31) |
| unambiguous semidirect product | (C2×C7)⋊(D3×C31) |
| Fitting, socle | C2×C3×C7×C31 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C22×C31 |
| Hall | C3×C7×C31 ⋊ C22 |
| Hall | C7×C31 ⋊ C2×D3 |
| Hall | C3×C31 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C31 |
| Sylow | C3 ⋊ C2×D7×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C31 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C31 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1302 |
744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D21×ΓL(1,𝔽32), D5×C31×D21, C2×C31×D105, … |
| maximal normal subgroup of | C2×D21×ΓL(1,𝔽32), C2×C5×C31×D21, C2×C7×C31×D21, … |
| maximal quotient of | D5×C31×D21, C2×C31×D105, C2×C5×C31×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2604, 63);