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C2×C3×D2849 #46803308

order34188
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2849
unambiguous semidirect product(C2×C11)⋊(C3×D259)

Splittings

Fitting, socleC2×C3×C7×C11×C37 ⋊ C2
derived, HallC7×C11×C37 ⋊ C22×C3
HallC3×C7×C11×C37 ⋊ C22
HallC3×C11×C37 ⋊ C2×D7
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D7
HallC7×C37 ⋊ C2×C3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×D77
HallC7×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C3×D77
HallC3×C11 ⋊ C2×D259
HallC3×C7 ⋊ C2×D407
SylowC11 ⋊ C2×C3×D259
SylowC7 ⋊ C2×C3×D407

Subgroups

subgroupG/H
center, hypercenterC2×C3D2849
commutator, cosocle, hypocenterC7×C11×C37C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C37C2
LCSG ▷ C7×C11×C37
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17094

Conjugacy classes & character table

8556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 180);