Finite Group Databasebeta

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C2×C3×C7×D407 #46803304

order34188
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D407
unambiguous semidirect product(C2×C11)⋊(C3×C7×D37)

Splittings

Fitting, socleC2×C3×C7×C11×C37 ⋊ C2
derived, HallC11×C37 ⋊ C22×C3×C7
HallC3×C7×C11×C37 ⋊ C22
HallC7×C11×C37 ⋊ C22×C3
HallC3×C11×C37 ⋊ C22×C7
HallC3×C7×C37 ⋊ C2×D11
HallC7×C37 ⋊ C2×C3×D11
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C3×C7×D11
HallC3×C11 ⋊ C2×C7×D37
SylowC11 ⋊ C2×C3×C7×D37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D407
commutator, cosocle, hypocenterC11×C37C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C37C2
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17094

Conjugacy classes & character table

8610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 176);