Finite Group Databasebeta

← Prev (#44415907) Next (#44415909) →

C7×D2085 #44415908

order29190
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2085
unambiguous semidirect productC3⋊(C7×D695)
unambiguous semidirect productC5⋊(C7×D417)
unambiguous semidirect productC139⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C139 ⋊ C2
derived, HallC3×C5×C139 ⋊ C2×C7
HallC5×C7×C139 ⋊ D3
HallC3×C7×C139 ⋊ D5
HallC7×C139 ⋊ D15
HallC5×C139 ⋊ D3×C7
HallC3×C139 ⋊ C7×D5
SylowC139 ⋊ C7×D15
HallC3×C5×C7 ⋊ D139
HallC5×C7 ⋊ D417
HallC3×C7 ⋊ D695
HallC3×C5 ⋊ C7×D139
SylowC5 ⋊ C7×D417
SylowC3 ⋊ C7×D695

Subgroups

subgroupG/H
center, hypercenterC7D2085
commutator, cosocle, hypocenterC3×C5×C139C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C139C2
LCSG ▷ C3×C5×C139
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14595

Conjugacy classes & character table

7308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29190, 18);