Finite Group Databasebeta

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C3×C7×C13×C11⋊C5 #28418525

order15015
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C7×C13)
unambiguous semidirect product(C3×C11)⋊(C5×C7×C13)
unambiguous semidirect product(C3×C7×C11)⋊(C5×C13)
unambiguous semidirect product(C3×C11×C13)⋊(C5×C7)
unambiguous semidirect product(C3×C7×C11×C13)⋊C5

Splittings

Fitting, socle, HallC3×C7×C11×C13 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C7×C13
HallC7×C11×C13 ⋊ C3×C5
HallC3×C11×C13 ⋊ C5×C7
HallC3×C7×C11 ⋊ C5×C13
HallC11×C13 ⋊ C3×C5×C7
HallC7×C11 ⋊ C3×C5×C13
HallC3×C11 ⋊ C5×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13C11⋊C5
commutator, cosocle, hypocenterC11C3×C5×C7×C13
FrattiniC1G
Fitting, socleC3×C7×C11×C13C5
LCSG ▷ C11
UCSC1 ◁ C3×C7×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1911 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15015, 2);