Finite Group Databasebeta

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C5×D3×C7×D19 #22547708

order7980
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C7×D19
unambiguous semidirect product(D3×C19)⋊(C2×C5×C7)
unambiguous semidirect product(C3×D19)⋊(C2×C5×C7)
unambiguous semidirect productD57⋊(C2×C5×C7)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C7D3×D19
commutator, hypocenterC3×C19C22×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C3×C19
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D9×D19, C5×D3×C7×D19⋊C3, C5×D3×#11716321, …
maximal normal subgroup ofC5×D3×C7×D19⋊C3, C5×D3×#11716321, C5×D3×#11716322, …
maximal quotient ofC5×C7×D9×D19, C3×C5×D3×C7×D19, C5×D3×C7×D57, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 133);