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C59×C22⋊(C13⋊C3) #22604198

order9204
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C59 · Schur multiplier (H2) = C2

Aliases

direct productC59×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C13⋊C3×C59)
unambiguous semidirect productC13⋊(A4×C59)
unambiguous semidirect product(C22×C59)⋊(C13⋊C3)
unambiguous semidirect product(C13×C59)⋊A4

Splittings

Fitting, socle, HallC22×C13×C59 ⋊ C3
derived, HallC22×C13 ⋊ C3×C59
HallC13×C59 ⋊ A4
HallC22×C59 ⋊ C13⋊C3
SylowC13 ⋊ A4×C59
SylowC22 ⋊ C13⋊C3×C59

Subgroups

subgroupG/H
center, hypercenterC59C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C3×C59
FrattiniC1G
Fitting, socleC22×C13×C59C3
LCSG ▷ C22×C13
UCSC1 ◁ C59

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1180 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C13⋊C3×C59, C3×C59×C22⋊(C13⋊C3)
maximal normal subgroup ofA4×C13⋊C3×C59, C3×C59×C22⋊(C13⋊C3)
maximal quotient ofC59×C22⋊(C13⋊C9), C3×C59×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9204, 31);