Finite Group Databasebeta

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C2×C7×D15×C71 #44447285

order29820
automorphism?
homologyAbelianization (H1) = C22×C7×C71 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D15×C71
unambiguous semidirect product(C2×C3)⋊(C7×D5×C71)
unambiguous semidirect product(C2×C5)⋊(D3×C7×C71)

Splittings

Fitting, socleC2×C3×C5×C7×C71 ⋊ C2
derived, HallC3×C5 ⋊ C22×C7×C71
HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C2×D3
HallC3×C7×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C22×C7
HallC5×C71 ⋊ C2×D3×C7
HallC3×C71 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C22×C71
HallC5×C7 ⋊ C2×D3×C71
HallC3×C7 ⋊ C2×D5×C71
SylowC5 ⋊ C2×D3×C7×C71
SylowC3 ⋊ C2×C7×D5×C71

Subgroups

subgroupG/H
center, hypercenterC2×C7×C71D15
commutator, cosocle, hypocenterC3×C5C22×C7×C71
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C71C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C7×C71

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14910

Conjugacy classes & character table

8946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 173);