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C7×D11×D39 #26046548

order12012
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D11×D39
unambiguous semidirect product(C3×D11)⋊(C7×D13)
unambiguous semidirect product(C13×D11)⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C22
derived, HallC3×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×D3
HallC3×C7×C13 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D3×C7
HallC7×C13 ⋊ D3×D11
HallC7×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D13
HallC3×C7 ⋊ D11×D13
SylowC13 ⋊ D3×C7×D11
SylowC11 ⋊ C2×C7×D39
SylowC3 ⋊ C7×D11×D13

Subgroups

subgroupG/H
center, hypercenterC7D11×D39
commutator, cosocle, hypocenterC3×C11×C13C22×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D11×D117, C7×D11×C3⋊(D13⋊C3), D11×C3⋊#10587716, …
maximal normal subgroup ofC7×D11×C3⋊(D13⋊C3), D11×C3⋊#10587716, D11×C3⋊#10587717, …
maximal quotient ofC7×D11×D117, C3×C7×D11×D39, C7×D33×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 138);