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C5×C7×D291 #35205016

order20370
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D291
unambiguous semidirect productC3⋊(C5×C7×D97)
unambiguous semidirect productC97⋊(C5×D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C97 ⋊ C2
derived, HallC3×C97 ⋊ C2×C5×C7
HallC5×C7×C97 ⋊ D3
HallC3×C7×C97 ⋊ C2×C5
HallC3×C5×C97 ⋊ C2×C7
HallC7×C97 ⋊ C5×D3
HallC5×C97 ⋊ D3×C7
HallC3×C5×C7 ⋊ D97
SylowC97 ⋊ C5×D3×C7
HallC3×C7 ⋊ C5×D97
HallC3×C5 ⋊ C7×D97
SylowC3 ⋊ C5×C7×D97

Subgroups

subgroupG/H
center, hypercenterC5×C7D291
commutator, cosocle, hypocenterC3×C97C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C97C2
LCSG ▷ C3×C97
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10185

Conjugacy classes & character table

5145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20370, 14);