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C3×C11⋊C5×D43 #28382003

order14190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×D43
unambiguous semidirect product(C3×C11×D43)⋊C5

Splittings

Fitting, socle, HallC3×C11×C43 ⋊ C2×C5
derived, HallC11×C43 ⋊ C2×C3×C5
HallC3×C43×C11⋊C5 ⋊ C2
HallC3×C11×D43 ⋊ C5
HallC43×C11⋊C5 ⋊ C2×C3
HallC11×D43 ⋊ C3×C5
HallC3×C43 ⋊ C2×C11⋊C5
SylowC43 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×D43
SylowC11 ⋊ C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D43
commutator, cosocle, hypocenterC11×C43C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C43C2×C5
LCSG ▷ C11×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1419

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D43×AGL(1,𝔽11), D43×C3⋊AGL(1,𝔽11), D3×C11⋊C5×D43, …
maximal normal subgroup ofC3×D43×AGL(1,𝔽11), D43×C3⋊AGL(1,𝔽11), D3×C11⋊C5×D43, …
maximal quotient ofC3×C11⋊C5×Dic43, C2×C3×C11⋊C5×D43

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 20);