Finite Group Databasebeta

← Prev (#45682136) Next (#45682138) →

C5×C7×D157⋊C3 #45682137

order32970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D157⋊C3
unambiguous semidirect productD157⋊(C3×C5×C7)
unambiguous semidirect product(C157⋊C3)⋊(C2×C5×C7)
unambiguous semidirect product(C5×D157)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C157 ⋊ C2×C3
derived, SylowC157 ⋊ C2×C3×C5×C7
HallC5×C7×C157⋊C3 ⋊ C2
HallC5×C7×D157 ⋊ C3
HallC7×C157⋊C3 ⋊ C2×C5
HallC5×C157⋊C3 ⋊ C2×C7
HallC7×D157 ⋊ C3×C5
HallC5×D157 ⋊ C3×C7
HallC7×C157 ⋊ C2×C3×C5
HallC5×C157 ⋊ C2×C3×C7
HallC157⋊C3 ⋊ C2×C5×C7
HallD157 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7D157⋊C3
commutator, cosocle, hypocenterC157C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C157C2×C3
LCSG ▷ C157
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5495

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 21);