Finite Group Databasebeta

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C7×D19×C11⋊C5 #28410702

order14630
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D19×C11⋊C5
unambiguous semidirect productC19⋊(C2×C7×C11⋊C5)
unambiguous semidirect product(C11×D19)⋊(C5×C7)
unambiguous semidirect product(C7×C11×D19)⋊C5

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C5
derived, HallC11×C19 ⋊ C2×C5×C7
HallC7×C19×C11⋊C5 ⋊ C2
HallC7×C11×D19 ⋊ C5
HallC19×C11⋊C5 ⋊ C2×C7
HallC11×D19 ⋊ C5×C7
HallC7×C19 ⋊ C2×C11⋊C5
HallC7×C11 ⋊ C5×D19
SylowC19 ⋊ C2×C7×C11⋊C5
SylowC11 ⋊ C5×C7×D19

Subgroups

subgroupG/H
center, hypercenterC7D19×C11⋊C5
commutator, cosocle, hypocenterC11×C19C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C19C2×C5
LCSG ▷ C11×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D19×AGL(1,𝔽11), D19×C7⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal normal subgroup ofC7×D19×AGL(1,𝔽11), D19×C7⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal quotient ofC7×C11⋊C5×Dic19, C2×C7×D19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14630, 18);