Finite Group Databasebeta

← Prev (#47977689) Next (#47977691) →

C2×C5×#16812971 #47977690

order35340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#16812971

Splittings

Fitting, socleC2×C5×C19×C31 ⋊ C2×C3
derived, HallC19×C31 ⋊ C22×C3×C5
HallC2×C5×C31×D19 ⋊ C3
HallC5×#13183715 ⋊ C22
HallC5×C19×C31 ⋊ C22×C3
HallC2×C31×D19 ⋊ C3×C5
Hall#13183715 ⋊ C22×C5
HallC2×C5×D19 ⋊ C31⋊C3
HallC5×C31 ⋊ C2×D19⋊C3
HallC5×C19 ⋊ C22×C31⋊C3
HallC2×D19 ⋊ C5×C31⋊C3
SylowC31 ⋊ C2×C5×D19⋊C3
SylowC19 ⋊ C22×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#16812971
commutator, cosocle, hypocenterC19×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C19×C31C2×C3
LCSG ▷ C19×C31
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5890

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 162);