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C7×#13133721⋊C3 #49088982

order35805
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#13133721⋊C3
unambiguous semidirect product#13133721⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C11×C31 ⋊ C3×C5
derived, HallC11×C31 ⋊ C3×C5×C7
HallC7×#13133721 ⋊ C3
HallC7×C11×C31⋊C3 ⋊ C5
Hall#13133721 ⋊ C3×C7
HallC11×C31⋊C3 ⋊ C5×C7
HallC7×C31⋊C3 ⋊ C11⋊C5
HallC7×C31 ⋊ C3×C11⋊C5
HallC31⋊C3 ⋊ C7×C11⋊C5
HallC7×C11 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C3×C7×C11⋊C5
SylowC11 ⋊ C7×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC7#13133721⋊C3
commutator, cosocle, hypocenterC11×C31C3×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C31C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2387

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35805, 14);