Finite Group Databasebeta

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C2×C3×D35×C71 #44447279

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C71 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D35×C71
unambiguous semidirect product(C2×C5)⋊(C3×D7×C71)

Splittings

Fitting, socleC2×C3×C5×C7×C71 ⋊ C2
derived, HallC5×C7 ⋊ C22×C3×C71
HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C22×C3
HallC3×C7×C71 ⋊ C2×D5
HallC3×C5×C71 ⋊ C2×D7
HallC7×C71 ⋊ C2×C3×D5
HallC5×C71 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C22×C71
HallC3×C7 ⋊ C2×D5×C71
HallC3×C5 ⋊ C2×D7×C71
SylowC7 ⋊ C2×C3×D5×C71
SylowC5 ⋊ C2×C3×D7×C71

Subgroups

subgroupG/H
center, hypercenterC2×C3×C71D35
commutator, cosocle, hypocenterC5×C7C22×C3×C71
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C71C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C71

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14910

Conjugacy classes & character table

8094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 167);