Finite Group Databasebeta

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C2×D21×C71⋊C5 #44447218

order29820
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D21×C71⋊C5
unambiguous semidirect product(C2×C3)⋊(D7×C71⋊C5)
unambiguous semidirect product(C2×C7)⋊(D3×C71⋊C5)
unambiguous semidirect product(C2×D21×C71)⋊C5

Splittings

Fitting, socleC2×C3×C7×C71 ⋊ C2×C5
derived, HallC3×C7×C71 ⋊ C22×C5
HallC3×C7×C71⋊C5 ⋊ C22
HallC2×D21×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ C2×D3
HallC3×C71⋊C5 ⋊ C2×D7
HallC7×C71 ⋊ C2×C5×D3
HallC3×C71 ⋊ C2×C5×D7
SylowC71 ⋊ C2×C5×D21
HallC3×C7 ⋊ C22×C71⋊C5
SylowC7 ⋊ C2×D3×C71⋊C5
SylowC3 ⋊ C2×D7×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D21×C71⋊C5
commutator, cosocle, hypocenterC3×C7×C71C22×C5
FrattiniC1G
Fitting, socleC2×C3×C7×C71C2×C5
LCSG ▷ C3×C7×C71
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2982

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 106);