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C2×C3×D613⋊C3 #36348192

order22068
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D613⋊C3
unambiguous semidirect productD613⋊(C2×C32)
unambiguous semidirect product(C613⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D613)⋊C32
unambiguous semidirect product(C2×C613⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D613)⋊C3

Splittings

Fitting, socleC2×C3×C613 ⋊ C2×C3
derived, SylowC613 ⋊ C22×C32
HallC3×C613⋊C3 ⋊ C22
HallC2×D613 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D613⋊C3
commutator, cosocle, hypocenterC613C22×C32
FrattiniC1G
Fitting, socleC2×C3×C613C2×C3
LCSG ▷ C613
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3678

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22068, 40);