Finite Group Databasebeta

← Prev (#22603328) Next (#22603330) →

C2×C5×C7×D65 #22603329

order9100
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D65
unambiguous semidirect product(C2×C5)⋊(C5×C7×D13)
unambiguous semidirect product(C2×C13)⋊(C5×C7×D5)

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2
derivedC5×C13 ⋊ C22×C5×C7
HallC52×C7×C13 ⋊ C22
HallC52×C13 ⋊ C22×C7
HallC52×C7 ⋊ C2×D13
HallC7×C13 ⋊ C2×C5×D5
SylowC52 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D65
commutator, hypocenterC5×C13C22×C5×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C13⋊#3874, C2×C5×C7×C5⋊(D13⋊C3), C2×C5×C5⋊#10587716, …
maximal normal subgroup ofC2×C5×C7×C5⋊(D13⋊C3), C2×C5×C5⋊#10587716, C2×C5×C5⋊#10587717, …
maximal quotient ofC5×D3×C7×D65, C2×C3×C5×C7×D65, C2×C5×C7×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9100, 114);