Finite Group Databasebeta

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C7×C13⋊C3×C11⋊C5 #28418530

order15015
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊C3×C11⋊C5
unambiguous semidirect productC11⋊(C5×C7×C13⋊C3)
unambiguous semidirect productC13⋊(C3×C7×C11⋊C5)
unambiguous semidirect product(C11×C13⋊C3)⋊(C5×C7)
unambiguous semidirect product(C13×C11⋊C5)⋊(C3×C7)
unambiguous semidirect product(C7×C11×C13⋊C3)⋊C5

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C3×C5
derived, HallC11×C13 ⋊ C3×C5×C7
HallC7×C13×C11⋊C5 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C7
HallC11×C13⋊C3 ⋊ C5×C7
HallC7×C13 ⋊ C3×C11⋊C5
HallC7×C11 ⋊ C5×C13⋊C3
SylowC13 ⋊ C3×C7×C11⋊C5
SylowC11 ⋊ C5×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C13⋊C3×C11⋊C5
commutator, cosocle, hypocenterC11×C13C3×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C13C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1001

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C7×C13⋊C3×C11⋊C5, C7×C11⋊C5×D13⋊C3, C7×C13⋊C3×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C7×C13⋊C3×C11⋊C5, C7×C11⋊C5×D13⋊C3, C7×C13⋊C3×AGL(1,𝔽11), …
maximal quotient ofC2×C7×C13⋊C3×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15015, 7);