Finite Group Databasebeta

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C2×C5×C11×C43⋊C3 #28381986

order14190
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×C43⋊C3
unambiguous semidirect product(C2×C43)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C43)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C43)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C43 ⋊ C3
derived, SylowC43 ⋊ C2×C3×C5×C11
HallC5×C11×C43 ⋊ C2×C3
HallC2×C11×C43 ⋊ C3×C5
HallC11×C43 ⋊ C2×C3×C5
HallC2×C5×C43 ⋊ C3×C11
HallC5×C43 ⋊ C2×C3×C11
HallC2×C43 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C43C3
LCSG ▷ C43
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4730

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C11×C43⋊C3, C5×C11×(C43⋊C3)⋊C4, C5×Dic11×C43⋊C3, …
maximal normal subgroup ofC4×C5×C11×C43⋊C3, C5×C11×(C43⋊C3)⋊C4, C5×Dic11×C43⋊C3, …
maximal quotient ofC4×C5×C11×C43⋊C3, C22×C5×C11×C43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 3);