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C11⋊C5×D133 #28410706

order14630
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D133
unambiguous semidirect productC7⋊(D19×C11⋊C5)
unambiguous semidirect productC19⋊(D7×C11⋊C5)
unambiguous semidirect product(C11×D133)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C19 ⋊ C2×C5
HallC7×C19×C11⋊C5 ⋊ C2
HallC11×D133 ⋊ C5
HallC19×C11⋊C5 ⋊ D7
HallC7×C11⋊C5 ⋊ D19
HallC11×C19 ⋊ C5×D7
HallC7×C19 ⋊ C2×C11⋊C5
HallC7×C11 ⋊ C5×D19
SylowC19 ⋊ D7×C11⋊C5
SylowC11 ⋊ C5×D133
SylowC7 ⋊ D19×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C19C2×C5
LCSG ▷ C7×C11×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽11)×D133, D133⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal normal subgroup ofAGL(1,𝔽11)×D133, D133⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal quotient ofC11⋊C5×Dic133, C2×C11⋊C5×D133

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14630, 22);