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C7×C5⋊(D157⋊C3) #45682153

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

Aliases

direct productC7×C5⋊(D157⋊C3)
unambiguous semidirect productC5⋊(C7×D157⋊C3)
unambiguous semidirect product(C157⋊C3)⋊(C7×D5)
unambiguous semidirect productD785⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C157 ⋊ C2×C3
derived, HallC5×C157 ⋊ C2×C3×C7
HallC5×C7×C157⋊C3 ⋊ C2
HallC7×D785 ⋊ C3
HallC7×C157⋊C3 ⋊ D5
HallC5×C157⋊C3 ⋊ C2×C7
HallD785 ⋊ C3×C7
HallC7×C157 ⋊ C3×D5
HallC157⋊C3 ⋊ C7×D5
SylowC157 ⋊ C3×C7×D5
HallC5×C7 ⋊ D157⋊C3
SylowC5 ⋊ C7×D157⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(D157⋊C3)
commutator, cosocle, hypocenterC5×C157C2×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C157C2×C3
LCSG ▷ C5×C157
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 37);