Finite Group Databasebeta

← Prev (#19129783) Next (#19129785) →

C2×C5×C7×D13⋊C3 #19129784

order5460
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C5×C7)
unambiguous semidirect product(C13⋊C3)⋊(C22×C5×C7)
unambiguous semidirect product(C2×D13)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C5×C7)
unambiguous semidirect product(C2×C5×D13)⋊(C3×C7)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C22×C3×C5×C7
HallC2×C5×C7×D13 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×C7×D13 ⋊ C3×C5
HallC7×C13⋊C3 ⋊ C22×C5
HallC2×C5×D13 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C22×C7
HallC7×C13 ⋊ C22×C3×C5
HallC5×C13 ⋊ C22×C3×C7
HallC2×D13 ⋊ C3×C5×C7
HallC13⋊C3 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D13⋊C3
commutator, hypocenterC13C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)×D13⋊C3, C5×D3×C7×D13⋊C3, C2×C3×C5×C7×D13⋊C3, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)×D13⋊C3, C2×C3×C5×C7×D13⋊C3, C2×C7×C25×D13⋊C3, …
maximal quotient ofC2×C5×C7×D13⋊C9, C5×D3×C7×D13⋊C3, C2×C3×C5×C7×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 126);