Finite Group Databasebeta

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D7×D15×C71 #44447251

order29820
automorphism?
homologyAbelianization (H1) = C22×C71 · Schur multiplier (H2) = C2

Aliases

direct productD7×D15×C71
unambiguous semidirect product(C3×D7)⋊(D5×C71)
unambiguous semidirect product(C5×D7)⋊(D3×C71)

Splittings

Fitting, socle, HallC3×C5×C7×C71 ⋊ C22
derived, HallC3×C5×C7 ⋊ C22×C71
HallC5×C7×C71 ⋊ C2×D3
HallC3×C7×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C2×D7
HallC7×C71 ⋊ C2×D15
HallC5×C71 ⋊ D3×D7
HallC3×C71 ⋊ D5×D7
HallC5×C7 ⋊ C2×D3×C71
HallC3×C7 ⋊ C2×D5×C71
HallC3×C5 ⋊ C2×D7×C71
SylowC7 ⋊ C2×D15×C71
SylowC5 ⋊ D3×D7×C71
SylowC3 ⋊ D5×D7×C71

Subgroups

subgroupG/H
center, hypercenterC71D7×D15
commutator, cosocle, hypocenterC3×C5×C7C22×C71
FrattiniC1G
Fitting, socleC3×C5×C7×C71C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C71

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7455

Conjugacy classes & character table

3195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 139);