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C11⋊C5×D129 #28382007

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

Aliases

direct productC11⋊C5×D129
unambiguous semidirect productC3⋊(C11⋊C5×D43)
unambiguous semidirect productC43⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D129)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C43 ⋊ C2×C5
HallC3×C43×C11⋊C5 ⋊ C2
HallC11×D129 ⋊ C5
HallC43×C11⋊C5 ⋊ D3
HallC11×C43 ⋊ C5×D3
HallC3×C11⋊C5 ⋊ D43
HallC3×C43 ⋊ C2×C11⋊C5
SylowC43 ⋊ D3×C11⋊C5
HallC3×C11 ⋊ C5×D43
SylowC11 ⋊ C5×D129
SylowC3 ⋊ C11⋊C5×D43

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C43C2×C5
LCSG ▷ C3×C11×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1419

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×D129, D129⋊AGL(1,𝔽11), D3×C11⋊C5×D43, …
maximal normal subgroup ofAGL(1,𝔽11)×D129, D129⋊AGL(1,𝔽11), D3×C11⋊C5×D43, …
maximal quotient ofC11⋊C5×Dic129, C2×C11⋊C5×D129

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 24);