Finite Group Databasebeta

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D7×C19×C11⋊C5 #28410705

order14630
automorphism?
homologyAbelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productD7×C19×C11⋊C5
unambiguous semidirect productC7⋊(C2×C19×C11⋊C5)
unambiguous semidirect product(C11×D7)⋊(C5×C19)
unambiguous semidirect product(C11×D7×C19)⋊C5

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C5×C19
HallC7×C19×C11⋊C5 ⋊ C2
HallC11×D7×C19 ⋊ C5
HallC7×C11⋊C5 ⋊ C2×C19
HallC11×C19 ⋊ C5×D7
HallC11×D7 ⋊ C5×C19
HallC7×C19 ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×D7×C19
SylowC7 ⋊ C2×C19×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC19D7×C11⋊C5
commutator, cosocle, hypocenterC7×C11C2×C5×C19
FrattiniC1G
Fitting, socleC7×C11×C19C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1463

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD7×C19×AGL(1,𝔽11), D7×C19⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal normal subgroup ofD7×C19×AGL(1,𝔽11), D7×C19⋊AGL(1,𝔽11), D7×D19×C11⋊C5, …
maximal quotient ofC19×Dic7×C11⋊C5, C2×D7×C19×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14630, 21);