Finite Group Databasebeta

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C11×C3⋊(Dic43⋊C7) #51432289

order39732
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(Dic43⋊C7)

Splittings

derived, HallC3×C43 ⋊ C4×C7×C11
HallC3×C11×C43⋊C7 ⋊ C4
HallC11×Dic129 ⋊ C7
HallC11×C43⋊C7 ⋊ Dic3
HallC3×C11×C43 ⋊ C4×C7
HallC3×C43⋊C7 ⋊ C4×C11
HallDic129 ⋊ C7×C11
HallC11×C43 ⋊ C7×Dic3
HallC43⋊C7 ⋊ C11×Dic3
SylowC43 ⋊ C7×C11×Dic3
HallC3×C11 ⋊ Dic43⋊C7
SylowC3 ⋊ C11×Dic43⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(D43⋊C7)
commutator, hypocenterC3×C43C4×C7×C11
FrattiniC2C11×C3⋊(D43⋊C7)
Fitting, socleC2×C3×C11×C43C2×C7
LCSG ▷ C3×C43
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 27);