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C5×C11×C22⋊(C13⋊C3) #22575179

order8580
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C5×C11×C13⋊C3)
unambiguous semidirect productC13⋊(C5×C11×A4)
unambiguous semidirect product(C22×C5)⋊(C11×C13⋊C3)
unambiguous semidirect product(C5×C13)⋊(C11×A4)
unambiguous semidirect product(C22×C5×C11)⋊(C13⋊C3)
unambiguous semidirect product(C5×C11×C13)⋊A4

Splittings

Fitting, socle, HallC22×C5×C11×C13 ⋊ C3
derived, HallC22×C13 ⋊ C3×C5×C11
HallC5×C11×C13 ⋊ A4
HallC22×C11×C13 ⋊ C3×C5
HallC22×C5×C13 ⋊ C3×C11
HallC22×C5×C11 ⋊ C13⋊C3
HallC11×C13 ⋊ C5×A4
HallC5×C13 ⋊ C11×A4
HallC22×C11 ⋊ C5×C13⋊C3
HallC22×C5 ⋊ C11×C13⋊C3
SylowC13 ⋊ C5×C11×A4
SylowC22 ⋊ C5×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C13C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×A4×C13⋊C3, C3×C5×C11×C22⋊(C13⋊C3)
maximal normal subgroup ofC5×C11×A4×C13⋊C3, C3×C5×C11×C22⋊(C13⋊C3)
maximal quotient ofC5×C11×C22⋊(C13⋊C9), C3×C5×C11×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 151);