Finite Group Databasebeta

← Prev (#36348999) Next (#36349001) →

C7×D17×C31⋊C3 #36349000

order22134
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D17×C31⋊C3
unambiguous semidirect productC17⋊(C2×C7×C31⋊C3)
unambiguous semidirect product(C31×D17)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C3
derived, HallC17×C31 ⋊ C2×C3×C7
HallC7×C17×C31⋊C3 ⋊ C2
HallC7×C31×D17 ⋊ C3
HallC17×C31⋊C3 ⋊ C2×C7
HallC31×D17 ⋊ C3×C7
HallC7×C31 ⋊ C3×D17
HallC7×C17 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×C7×D17
SylowC17 ⋊ C2×C7×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D17×C31⋊C3
commutator, cosocle, hypocenterC17×C31C2×C3×C7
FrattiniC1G
Fitting, socleC7×C17×C31C2×C3
LCSG ▷ C17×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22134, 25);