Finite Group Databasebeta

← Prev (#19129883) Next (#19129885) →

C2×C3×C7×D65 #19129884

order5460
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D65
unambiguous semidirect product(C2×C5)⋊(C3×C7×D13)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, HallC5×C13 ⋊ C22×C3×C7
HallC3×C5×C7×C13 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC3×C7×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C22×C7
HallC3×C5×C7 ⋊ C2×D13
HallC7×C13 ⋊ C2×C3×D5
HallC3×C13 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×C3×D13
HallC3×C5 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C3×C7×D5
SylowC5 ⋊ C2×C3×C7×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D65
commutator, hypocenterC5×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C5⋊(D13⋊C9), C2×C5⋊#13109896, C2×C5⋊#13109897, …
maximal normal subgroup ofC2×C7×C5⋊(D13⋊C9), C2×C5⋊#13109896, C2×C5⋊#13109897, …
maximal quotient ofC2×C7×C9×D65, C3×D3×C7×D65, C2×C3×C7×D195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 226);