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C2×C3×D577⋊C3 #35209396

order20772
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×D577⋊C3
unambiguous semidirect productD577⋊(C2×C32)
unambiguous semidirect product(C577⋊C3)⋊(C22×C3)
unambiguous semidirect product(C2×D577)⋊C32
unambiguous semidirect product(C2×C577⋊C3)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D577)⋊C3

Splittings

Fitting, socleC2×C3×C577 ⋊ C2×C3
derived, SylowC577 ⋊ C22×C32
HallC3×C577⋊C3 ⋊ C22
HallC2×D577 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC2×C3D577⋊C3
commutator, cosocle, hypocenterC577C22×C32
FrattiniC1G
Fitting, socleC2×C3×C577C2×C3
LCSG ▷ C577
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20772, 40);