Finite Group Databasebeta

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C37×D21⋊D11 #46803289

order34188
automorphism?
homologyAbelianization (H1) = C22×C37 · Schur multiplier (H2) = C2

Aliases

direct productC37×D21⋊D11
unambiguous semidirect productD21⋊(D11×C37)
unambiguous semidirect productD33⋊(D7×C37)
unambiguous semidirect productD77⋊(D3×C37)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C22
derived, HallC3×C7×C11 ⋊ C22×C37
HallC7×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D7
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ D3×D7
HallC7×C37 ⋊ D3×D11
HallC3×C37 ⋊ D7×D11
HallC7×C11 ⋊ C2×D3×C37
HallC3×C11 ⋊ C2×D7×C37
HallC3×C7 ⋊ C2×D11×C37
SylowC11 ⋊ D3×D7×C37
SylowC7 ⋊ D3×D11×C37
SylowC3 ⋊ D7×D11×C37

Subgroups

subgroupG/H
center, hypercenterC37D21⋊D11
commutator, cosocle, hypocenterC3×C7×C11C22×C37
FrattiniC1G
Fitting, socleC3×C7×C11×C37C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

2775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 161);