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C13×C5⋊(D7⋊C9) #22551208

order8190
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊(D7⋊C9)
unambiguous semidirect productC5⋊(C13×D7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(D5×C13)
unambiguous semidirect productD35⋊(C9×C13)

Splittings

derived, HallC5×C7 ⋊ C2×C9×C13
HallC5×C13×C7⋊C9 ⋊ C2
HallC13×D35 ⋊ C9
HallC13×C7⋊C9 ⋊ D5
HallC5×C7×C13 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C13
HallC7×C13 ⋊ C9×D5
HallD35 ⋊ C9×C13
HallC5×C13 ⋊ D7⋊C9
HallC7⋊C9 ⋊ D5×C13
SylowC7 ⋊ C9×D5×C13
SylowC5 ⋊ C13×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C13C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C2×C9×C13
FrattiniC3C13×C5⋊AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

663 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×C5⋊(D7⋊C9), D5×C13×D7⋊C9, (C5⋊(D7⋊C9))⋊D13, …
maximal normal subgroup ofD13×C5⋊(D7⋊C9), D5×C13×D7⋊C9, (C5⋊(D7⋊C9))⋊D13, …
maximal quotient ofC13×(C7⋊C9)⋊Dic5, C2×C13×C5⋊(D7⋊C9)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 42);