Finite Group Databasebeta

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C2×C3×D2695 #44568428

order32340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2695
unambiguous semidirect product(C2×C5)⋊(C3×D539)
unambiguous semidirect product(C2×C11)⋊(C3×D245)

Splittings

FittingC2×C3×C5×C11×C49 ⋊ C2
derived, HallC5×C11×C49 ⋊ C22×C3
HallC3×C5×C11×C49 ⋊ C22
HallC3×C11×C49 ⋊ C2×D5
HallC3×C5×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×C3×D5
HallC5×C49 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D49
HallC3×C49 ⋊ C2×D55
HallC5×C11 ⋊ C2×C3×D49
SylowC49 ⋊ C2×C3×D55
HallC3×C11 ⋊ C2×D245
HallC3×C5 ⋊ C2×D539
SylowC11 ⋊ C2×C3×D245
SylowC5 ⋊ C2×C3×D539

Subgroups

subgroupG/H
center, hypercenterC2×C3D2695
commutator, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7C2×C3×D385
FittingC2×C3×C5×C11×C49C2
socleC2×C3×C5×C7×C11D7
LCSG ▷ C5×C11×C49
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

8094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 130);