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C5×D2037 #35205018

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

Aliases

direct productC5×D2037
unambiguous semidirect productC3⋊(C5×D679)
unambiguous semidirect productC7⋊(C5×D291)
unambiguous semidirect productC97⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C97 ⋊ C2
derived, HallC3×C7×C97 ⋊ C2×C5
HallC5×C7×C97 ⋊ D3
HallC3×C5×C97 ⋊ D7
HallC7×C97 ⋊ C5×D3
HallC5×C97 ⋊ D21
HallC3×C97 ⋊ C5×D7
HallC3×C5×C7 ⋊ D97
SylowC97 ⋊ C5×D21
HallC5×C7 ⋊ D291
HallC3×C7 ⋊ C5×D97
HallC3×C5 ⋊ D679
SylowC7 ⋊ C5×D291
SylowC3 ⋊ C5×D679

Subgroups

subgroupG/H
center, hypercenterC5D2037
commutator, cosocle, hypocenterC3×C7×C97C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C97C2
LCSG ▷ C3×C7×C97
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10185

Conjugacy classes & character table

5100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20370, 16);