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C5×C13×C22⋊(C13⋊C3) #23778598

order10140
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C13×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C5×C13×C13⋊C3)
unambiguous semidirect productC13⋊(C5×A4×C13)
unambiguous semidirect product(C22×C5)⋊(C13×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(A4×C13)

Splittings

Fitting, socle, HallC22×C5×C132 ⋊ C3
derivedC22×C13 ⋊ C3×C5×C13
HallC5×C132 ⋊ A4
HallC22×C132 ⋊ C3×C5
SylowC132 ⋊ C5×A4
HallC22×C5 ⋊ C13×C13⋊C3
SylowC22 ⋊ C5×C13×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C13C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C5×C13
FrattiniC1G
Fitting, socleC22×C5×C132C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×A4×C13×C13⋊C3, C5×C13⋊C3×C22⋊(C13⋊C3), C5×#92788⋊A4, …
maximal normal subgroup ofC5×A4×C13×C13⋊C3, C5×C13⋊C3×C22⋊(C13⋊C3), C5×#92788⋊A4, …
maximal quotient ofC5×C13×C22⋊(C13⋊C9), C3×C5×C13×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 256);