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C5×D11×C43⋊C3 #28382011

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

Aliases

direct productC5×D11×C43⋊C3
unambiguous semidirect product(C5×D11×C43)⋊C3

Splittings

Fitting, socle, HallC5×C11×C43 ⋊ C2×C3
derived, HallC11×C43 ⋊ C2×C3×C5
HallC5×C11×C43⋊C3 ⋊ C2
HallC5×D11×C43 ⋊ C3
HallC11×C43⋊C3 ⋊ C2×C5
HallD11×C43 ⋊ C3×C5
HallC5×C43 ⋊ C3×D11
HallC5×C11 ⋊ C2×C43⋊C3
SylowC43 ⋊ C3×C5×D11
SylowC11 ⋊ C2×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×C43⋊C3
commutator, cosocle, hypocenterC11×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C43C2×C3
LCSG ▷ C11×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×D43⋊C3, D11×C5⋊(D43⋊C3), D5×D11×C43⋊C3, …
maximal normal subgroup ofC5×D11×D43⋊C3, D11×C5⋊(D43⋊C3), D5×D11×C43⋊C3, …
maximal quotient ofC5×Dic11×C43⋊C3, C2×C5×D11×C43⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 28);