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C5×#20268653 #45682147

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

Aliases

direct productC5×#20268653

Splittings

Fitting, socle, HallC5×C7×C157 ⋊ C2×C3
derived, HallC7×C157 ⋊ C2×C3×C5
HallC5×#15693073 ⋊ C2
HallC5×D1099 ⋊ C3
Hall#15693073 ⋊ C2×C5
HallD1099 ⋊ C3×C5
HallC5×C157 ⋊ AGL(1,𝔽7)
SylowC157 ⋊ C5×AGL(1,𝔽7)
HallC5×C7 ⋊ D157⋊C3
SylowC7 ⋊ C5×D157⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#20268653
commutator, cosocle, hypocenterC7×C157C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C157C2×C3
LCSG ▷ C7×C157
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 31);