Finite Group Databasebeta

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C2×C3×C7×D209 #31798347

order17556
isoclinismisoclinic class of D209
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D209
unambiguous semidirect product(C2×C11)⋊(C3×C7×D19)

Splittings

Fitting, socleC2×C3×C7×C11×C19 ⋊ C2
derived, HallC11×C19 ⋊ C22×C3×C7
HallC3×C7×C11×C19 ⋊ C22
HallC7×C11×C19 ⋊ C22×C3
HallC3×C11×C19 ⋊ C22×C7
HallC3×C7×C19 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D19
HallC7×C19 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D19
HallC3×C19 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D19
SylowC19 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×D19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D209
commutator, cosocle, hypocenterC11×C19C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C19C2
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8778

Conjugacy classes & character table

4452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 162);