Finite Group Databasebeta

← Prev (#27164973) Next (#27164975) →

C2×C72×D65 #27164974

order12740
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D65
unambiguous semidirect product(C2×C5)⋊(C72×D13)
unambiguous semidirect product(C2×C13)⋊(C72×D5)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2
derived, HallC5×C13 ⋊ C22×C72
HallC5×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×D5
HallC5×C72 ⋊ C2×D13
SylowC13 ⋊ C2×C72×D5
SylowC5 ⋊ C2×C72×D13

Subgroups

subgroupG/H
center, hypercenterC2×C72D65
commutator, cosocle, hypocenterC5×C13C22×C72
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C72

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3332 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C72×C5⋊(D13⋊C3), C2×C7×C5⋊#10587716, C2×C7×C5⋊#10587717, …
maximal normal subgroup ofC2×C72×C5⋊(D13⋊C3), C2×C7×C5⋊#10587716, C2×C7×C5⋊#10587717, …
maximal quotient ofD3×C72×D65, C2×C3×C72×D65, C2×C72×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12740, 104);