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D3×C7×C67⋊C11 #44526248

order30954
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C67⋊C11
unambiguous semidirect productC3⋊(C2×C7×C67⋊C11)
unambiguous semidirect product(D3×C67)⋊(C7×C11)
unambiguous semidirect product(D3×C7×C67)⋊C11

Splittings

Fitting, socle, HallC3×C7×C67 ⋊ C2×C11
derived, HallC3×C67 ⋊ C2×C7×C11
HallC3×C7×C67⋊C11 ⋊ C2
HallD3×C7×C67 ⋊ C11
HallC3×C67⋊C11 ⋊ C2×C7
HallC7×C67 ⋊ D3×C11
HallD3×C67 ⋊ C7×C11
SylowC67 ⋊ D3×C7×C11
HallC3×C7 ⋊ C2×C67⋊C11
SylowC3 ⋊ C2×C7×C67⋊C11

Subgroups

subgroupG/H
center, hypercenterC7D3×C67⋊C11
commutator, cosocle, hypocenterC3×C67C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C67C2×C11
LCSG ▷ C3×C67
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1407

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 29);