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D7×C5⋊(D19⋊C3) #22547665

order7980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD7×C5⋊(D19⋊C3)
unambiguous semidirect product(D7×C19⋊C3)⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD7×D95 ⋊ C3
HallC5×C7×C19⋊C3 ⋊ C22
HallC7×C19⋊C3 ⋊ C2×D5
HallC5×C19⋊C3 ⋊ C2×D7
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×C3×D7
HallC19⋊C3 ⋊ D5×D7
HallC5×C7 ⋊ C2×D19⋊C3
SylowC19 ⋊ C3×D5×D7
SylowC7 ⋊ C2×C5⋊(D19⋊C3)
SylowC5 ⋊ D7×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14558803⋊D5, #14558804⋊D5, AGL(1,𝔽7)×C5⋊(D19⋊C3), …
maximal normal subgroup of#14558803⋊D5, #14558804⋊D5, AGL(1,𝔽7)×C5⋊(D19⋊C3), …
maximal quotient ofD7×C5⋊(#4294⋊C2), C3×D7×C5⋊(D19⋊C3), D7×C3⋊(C5⋊(D19⋊C3)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 90);