Finite Group Databasebeta

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C5×C11×D43⋊C3 #28382010

order14190
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D43⋊C3
unambiguous semidirect productD43⋊(C3×C5×C11)
unambiguous semidirect product(C43⋊C3)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D43)⋊(C3×C11)
unambiguous semidirect product(C5×C11×D43)⋊C3

Splittings

Fitting, socle, HallC5×C11×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C2×C3×C5×C11
HallC5×C11×C43⋊C3 ⋊ C2
HallC5×C11×D43 ⋊ C3
HallC11×C43⋊C3 ⋊ C2×C5
HallC11×D43 ⋊ C3×C5
HallC5×C43⋊C3 ⋊ C2×C11
HallC11×C43 ⋊ C2×C3×C5
HallC5×D43 ⋊ C3×C11
HallC5×C43 ⋊ C2×C3×C11
HallC43⋊C3 ⋊ C2×C5×C11
HallD43 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11D43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×D43⋊C3, D5×C11×D43⋊C3, D55×D43⋊C3, …
maximal normal subgroup ofC5×D11×D43⋊C3, D5×C11×D43⋊C3, D55×D43⋊C3, …
maximal quotient ofC5×C11×(C43⋊C3)⋊C4, C2×C5×C11×D43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 27);