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C5×D21⋊D19 #22547713

order7980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D21⋊D19
unambiguous semidirect productD21⋊(C5×D19)
unambiguous semidirect productD57⋊(C5×D7)
unambiguous semidirect productD133⋊(C5×D3)

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC3×C7×C19 ⋊ C22×C5
HallC5×C7×C19 ⋊ C2×D3
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ C2×C5×D3
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ D3×D7
HallC3×C19 ⋊ C2×C5×D7
HallC5×C7 ⋊ D3×D19
HallC3×C7 ⋊ C2×C5×D19
SylowC19 ⋊ C5×D3×D7
HallC3×C5 ⋊ D7×D19
SylowC7 ⋊ C5×D3×D19
SylowC3 ⋊ C5×D7×D19

Subgroups

subgroupG/H
center, hypercenterC5D21⋊D19
commutator, hypocenterC3×C7×C19C22×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C3×C7×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

615 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D63⋊D19, C5×#11716327⋊D3, C5×#11716328⋊D3, …
maximal normal subgroup ofC5×#11716327⋊D3, C5×#11716328⋊D3, C5×(C3⋊AGL(1,𝔽7))⋊D19, …
maximal quotient ofC5×D63⋊D19, C3×C5×D21⋊D19, C5×D57⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 138);