Finite Group Databasebeta

← Prev (#49146265) Next (#49146267) →

C17×C31×D35 #49146266

order36890
automorphism?
homologyAbelianization (H1) = C2×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC17×C31×D35
unambiguous semidirect productC5⋊(D7×C17×C31)
unambiguous semidirect productC7⋊(D5×C17×C31)

Splittings

Fitting, socle, HallC5×C7×C17×C31 ⋊ C2
derived, HallC5×C7 ⋊ C2×C17×C31
HallC7×C17×C31 ⋊ D5
HallC5×C17×C31 ⋊ D7
HallC5×C7×C31 ⋊ C2×C17
HallC5×C7×C17 ⋊ C2×C31
HallC7×C31 ⋊ D5×C17
HallC5×C31 ⋊ D7×C17
HallC7×C17 ⋊ D5×C31
HallC5×C17 ⋊ D7×C31
SylowC7 ⋊ D5×C17×C31
SylowC5 ⋊ D7×C17×C31

Subgroups

subgroupG/H
center, hypercenterC17×C31D35
commutator, cosocle, hypocenterC5×C7C2×C17×C31
FrattiniC1G
Fitting, socleC5×C7×C17×C31C2
LCSG ▷ C5×C7
UCSC1 ◁ C17×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18445

Conjugacy classes & character table

10013 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 14);