Finite Group Databasebeta

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C2×C31×D65 #22549008

order8060
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31×D65
unambiguous semidirect product(C2×C5)⋊(D13×C31)
unambiguous semidirect product(C2×C13)⋊(D5×C31)

Splittings

Fitting, socleC2×C5×C13×C31 ⋊ C2
derived, HallC5×C13 ⋊ C22×C31
HallC5×C13×C31 ⋊ C22
HallC13×C31 ⋊ C2×D5
HallC5×C31 ⋊ C2×D13
SylowC13 ⋊ C2×D5×C31
SylowC5 ⋊ C2×D13×C31

Subgroups

subgroupG/H
center, hypercenterC2×C31D65
commutator, hypocenterC5×C13C22×C31
FrattiniC1G
Fitting, socleC2×C5×C13×C31C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C31

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C31×C5⋊(D13⋊C3), C2×C5⋊#14559027, C2×C5⋊#14559026, …
maximal normal subgroup ofC2×C31×C5⋊(D13⋊C3), C2×C5⋊#14559027, C2×C5⋊#14559026, …
maximal quotient ofD3×C31×D65, C2×C3×C31×D65, C2×C31×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8060, 41);