Finite Group Databasebeta

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C2×C72×D61⋊C3 #49089908

order35868
automorphism?
homologyAbelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D61⋊C3
unambiguous semidirect productD61⋊(C2×C3×C72)
unambiguous semidirect product(C61⋊C3)⋊(C22×C72)
unambiguous semidirect product(C2×D61)⋊(C3×C72)
unambiguous semidirect product(C2×C61⋊C3)⋊(C2×C72)

Splittings

Fitting, socleC2×C72×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C22×C3×C72
HallC2×C72×D61 ⋊ C3
HallC72×C61⋊C3 ⋊ C22
HallC72×C61 ⋊ C22×C3
HallC2×D61 ⋊ C3×C72
HallC61⋊C3 ⋊ C22×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72D61⋊C3
commutator, cosocle, hypocenterC61C22×C3×C72
FrattiniC1G
Fitting, socleC2×C72×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C2×C72

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5978

Conjugacy classes & character table

1568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35868, 260);