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C2×C19⋊C3×D35 #22547696

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

Aliases

direct productC2×C19⋊C3×D35
unambiguous semidirect product(C2×C5)⋊(D7×C19⋊C3)

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C22×C3
HallC2×C19×D35 ⋊ 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
HallC5×C7 ⋊ C22×C19⋊C3
SylowC19 ⋊ C2×C3×D35
SylowC7 ⋊ C2×D5×C19⋊C3
SylowC5 ⋊ C2×D7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C19⋊C3×D35
commutator, hypocenterC5×C7×C19C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5⋊#14558803, C2×C5⋊#14558804, C2×C19⋊C3×C5⋊AGL(1,𝔽7), …
maximal normal subgroup ofC2×C5⋊#14558803, C2×C5⋊#14558804, C2×C19⋊C3×C5⋊AGL(1,𝔽7), …
maximal quotient ofC2×D35×#4294, D3×C19⋊C3×D35, C2×C3×C19⋊C3×D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 121);