Finite Group Databasebeta

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C31×D595 #49146268

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

Aliases

direct productC31×D595
unambiguous semidirect productC5⋊(C31×D119)
unambiguous semidirect productC7⋊(C31×D85)
unambiguous semidirect productC17⋊(C31×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C31 ⋊ C2
derived, HallC5×C7×C17 ⋊ C2×C31
HallC7×C17×C31 ⋊ D5
HallC5×C17×C31 ⋊ D7
HallC5×C7×C31 ⋊ D17
HallC17×C31 ⋊ D35
HallC7×C31 ⋊ D85
HallC5×C31 ⋊ D119
HallC7×C17 ⋊ D5×C31
HallC5×C17 ⋊ D7×C31
HallC5×C7 ⋊ C31×D17
SylowC17 ⋊ C31×D35
SylowC7 ⋊ C31×D85
SylowC5 ⋊ C31×D119

Subgroups

subgroupG/H
center, hypercenterC31D595
commutator, cosocle, hypocenterC5×C7×C17C2×C31
FrattiniC1G
Fitting, socleC5×C7×C17×C31C2
LCSG ▷ C5×C7×C17
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18445

Conjugacy classes & character table

9269 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 16);