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D35×D13⋊C3 #19129779

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

Aliases

direct productD35×D13⋊C3
unambiguous semidirect productD13⋊(C3×D35)
unambiguous semidirect product(C5×D13⋊C3)⋊D7
unambiguous semidirect product(C7×D13⋊C3)⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C3
HallD13×D35 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC7×C13⋊C3 ⋊ C2×D5
HallC5×C13⋊C3 ⋊ C2×D7
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D7
HallC13⋊C3 ⋊ C2×D35
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×C3×D35
SylowC7 ⋊ D5×D13⋊C3
SylowC5 ⋊ D7×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×C5⋊AGL(1,𝔽7), C3×D35×D13⋊C3, D13⋊C3×D105, …
maximal normal subgroup ofD13⋊C3×C5⋊AGL(1,𝔽7), C3×D35×D13⋊C3, C5×D35×D13⋊C3, …
maximal quotient ofD35×D13⋊C9, C3×D35×D13⋊C3, D13⋊C3×D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 121);