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C7×D2355 #45682134

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

Aliases

direct productC7×D2355
unambiguous semidirect productC3⋊(C7×D785)
unambiguous semidirect productC5⋊(C7×D471)
unambiguous semidirect productC157⋊(C7×D15)

Splittings

Fitting, socle, HallC3×C5×C7×C157 ⋊ C2
derived, HallC3×C5×C157 ⋊ C2×C7
HallC5×C7×C157 ⋊ D3
HallC3×C7×C157 ⋊ D5
HallC7×C157 ⋊ D15
HallC5×C157 ⋊ D3×C7
HallC3×C157 ⋊ C7×D5
SylowC157 ⋊ C7×D15
HallC3×C5×C7 ⋊ D157
HallC5×C7 ⋊ D471
HallC3×C7 ⋊ D785
HallC3×C5 ⋊ C7×D157
SylowC5 ⋊ C7×D471
SylowC3 ⋊ C7×D785

Subgroups

subgroupG/H
center, hypercenterC7D2355
commutator, cosocle, hypocenterC3×C5×C157C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C157C2
LCSG ▷ C3×C5×C157
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16485

Conjugacy classes & character table

8253 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 18);