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C13×C22⋊(C43⋊C3) #20269484

order6708
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C13×C43⋊C3)
unambiguous semidirect productC43⋊(A4×C13)

Splittings

Fitting, socle, HallC22×C13×C43 ⋊ C3
derived, HallC22×C43 ⋊ C3×C13
HallC13×C43 ⋊ A4
HallC22×C13 ⋊ C43⋊C3
SylowC43 ⋊ A4×C13
SylowC22 ⋊ C13×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C22⋊(C43⋊C3)
commutator, hypocenterC22×C43C3×C13
FrattiniC1G
Fitting, socleC22×C13×C43C3
LCSG ▷ C22×C43
UCSC1 ◁ C13

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C13×C43⋊C3, C13⋊C3×C22⋊(C43⋊C3), #13131976⋊A4, …
maximal normal subgroup ofA4×C13×C43⋊C3, C13⋊C3×C22⋊(C43⋊C3), #13131976⋊A4, …
maximal quotient ofC13×C22⋊(C43⋊C9), C3×C13×C22⋊(C43⋊C3), C5×C13×C22⋊(C43⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6708, 64);