Finite Group Databasebeta

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C2×C3×D2737 #45659331

order32844
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2737
unambiguous semidirect product(C2×C17)⋊(C3×D161)
unambiguous semidirect product(C2×C23)⋊(C3×D119)

Splittings

Fitting, socleC2×C3×C7×C17×C23 ⋊ C2
derived, HallC7×C17×C23 ⋊ C22×C3
HallC3×C7×C17×C23 ⋊ C22
HallC3×C17×C23 ⋊ C2×D7
HallC3×C7×C23 ⋊ C2×D17
HallC17×C23 ⋊ C2×C3×D7
HallC3×C7×C17 ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D17
HallC7×C17 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×D119
HallC3×C17 ⋊ C2×D161
SylowC23 ⋊ C2×C3×D119
HallC3×C7 ⋊ C2×D391
SylowC17 ⋊ C2×C3×D161
SylowC7 ⋊ C2×C3×D391

Subgroups

subgroupG/H
center, hypercenterC2×C3D2737
commutator, cosocle, hypocenterC7×C17×C23C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C17×C23C2
LCSG ▷ C7×C17×C23
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16422

Conjugacy classes & character table

8220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 96);