Finite Group Databasebeta

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C2×C7×D741 #35209208

order20748
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D741
unambiguous semidirect product(C2×C3)⋊(C7×D247)
unambiguous semidirect product(C2×C13)⋊(C7×D57)
unambiguous semidirect product(C2×C19)⋊(C7×D39)

Splittings

Fitting, socleC2×C3×C7×C13×C19 ⋊ C2
derived, HallC3×C13×C19 ⋊ C22×C7
HallC3×C7×C13×C19 ⋊ C22
HallC7×C13×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D13
HallC3×C7×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×D3×C7
HallC7×C19 ⋊ C2×D39
HallC7×C13 ⋊ C2×D57
HallC3×C19 ⋊ C2×C7×D13
HallC3×C13 ⋊ C2×C7×D19
HallC3×C7 ⋊ C2×D247
SylowC19 ⋊ C2×C7×D39
SylowC13 ⋊ C2×C7×D57
SylowC3 ⋊ C2×C7×D247

Subgroups

subgroupG/H
center, hypercenterC2×C7D741
commutator, cosocle, hypocenterC3×C13×C19C22×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C19C2
LCSG ▷ C3×C13×C19
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10374

Conjugacy classes & character table

5208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 436);