Finite Group Databasebeta

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C7×D11×D111 #46803266

order34188
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D11×D111
unambiguous semidirect product(C3×D11)⋊(C7×D37)
unambiguous semidirect product(D11×C37)⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C22
derived, HallC3×C11×C37 ⋊ C22×C7
HallC7×C11×C37 ⋊ C2×D3
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×D3×C7
HallC7×C37 ⋊ D3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×D111
SylowC37 ⋊ D3×C7×D11
HallC3×C11 ⋊ C2×C7×D37
HallC3×C7 ⋊ D11×D37
SylowC11 ⋊ C2×C7×D111
SylowC3 ⋊ C7×D11×D37

Subgroups

subgroupG/H
center, hypercenterC7D11×D111
commutator, cosocle, hypocenterC3×C11×C37C22×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C37C22
LCSG ▷ C3×C11×C37
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

2793 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 138);