Finite Group Databasebeta

← Prev (#19129752) Next (#19129754) →

C7×D5×D13⋊C3 #19129753

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

Aliases

direct productC7×D5×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×D5)
unambiguous semidirect product(D5×D13)⋊(C3×C7)
unambiguous semidirect product(C5×D13⋊C3)⋊(C2×C7)
unambiguous semidirect product(D5×C13⋊C3)⋊(C2×C7)
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC5×C7×C13 ⋊ C22×C3
derived, HallC5×C13 ⋊ C22×C3×C7
HallC7×D5×D13 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC7×C13⋊C3 ⋊ C2×D5
HallD5×D13 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C22×C7
HallC7×C13 ⋊ C2×C3×D5
HallC13⋊C3 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D5
SylowC5 ⋊ C2×C7×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D5×D13⋊C3
commutator, hypocenterC5×C13C22×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C13C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)×D13⋊C3, C3×C7×D5×D13⋊C3, C7×D15×D13⋊C3, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)×D13⋊C3, C3×C7×D5×D13⋊C3, C5×C7×D5×D13⋊C3, …
maximal quotient ofC7×D5×D13⋊C9, C3×C7×D5×D13⋊C3, C7×D15×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 95);