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C3×D7×D407 #46803259

order34188
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D7×D407

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C22
derived, HallC7×C11×C37 ⋊ C22×C3
HallC3×C11×C37 ⋊ C2×D7
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D7
HallC7×C37 ⋊ C2×C3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ D7×D11
HallC7×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C3×D7×D11
HallC3×C11 ⋊ D7×D37
HallC3×C7 ⋊ C2×D407
SylowC11 ⋊ C3×D7×D37
SylowC7 ⋊ C2×C3×D407

Subgroups

subgroupG/H
center, hypercenterC3D7×D407
commutator, cosocle, hypocenterC7×C11×C37C22×C3
FrattiniC1G
Fitting, socleC3×C7×C11×C37C22
LCSG ▷ C7×C11×C37
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

3075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 131);