Finite Group Databasebeta

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C29×D665 #50310739

order38570
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D665
unambiguous semidirect productC5⋊(C29×D133)
unambiguous semidirect productC7⋊(C29×D95)
unambiguous semidirect productC19⋊(C29×D35)

Splittings

Fitting, socle, HallC5×C7×C19×C29 ⋊ C2
derived, HallC5×C7×C19 ⋊ C2×C29
HallC7×C19×C29 ⋊ D5
HallC5×C19×C29 ⋊ D7
HallC5×C7×C29 ⋊ D19
HallC19×C29 ⋊ D35
HallC7×C29 ⋊ D95
HallC5×C29 ⋊ D133
HallC7×C19 ⋊ D5×C29
HallC5×C19 ⋊ D7×C29
HallC5×C7 ⋊ C29×D19
SylowC19 ⋊ C29×D35
SylowC7 ⋊ C29×D95
SylowC5 ⋊ C29×D133

Subgroups

subgroupG/H
center, hypercenterC29D665
commutator, cosocle, hypocenterC5×C7×C19C2×C29
FrattiniC1G
Fitting, socleC5×C7×C19×C29C2
LCSG ▷ C5×C7×C19
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19285

Conjugacy classes & character table

9686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38570, 16);