Finite Group Databasebeta

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C7×D5×D57 #22547725

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

Aliases

direct productC7×D5×D57
unambiguous semidirect product(C3×D5)⋊(C7×D19)
unambiguous semidirect product(D5×C19)⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C22
derived, HallC3×C5×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC7×C19 ⋊ D3×D5
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×D3×C7
HallC3×C19 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×D57
HallC3×C7 ⋊ D5×D19
SylowC19 ⋊ D3×C7×D5
HallC3×C5 ⋊ C2×C7×D19
SylowC5 ⋊ C2×C7×D57
SylowC3 ⋊ C7×D5×D19

Subgroups

subgroupG/H
center, hypercenterC7D5×D57
commutator, hypocenterC3×C5×C19C22×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C19C22
LCSG ▷ C3×C5×C19
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D5×D171, C7×D5×C3⋊(D19⋊C3), D5×C3⋊#11716321, …
maximal normal subgroup ofC7×D5×C3⋊(D19⋊C3), D5×C3⋊#11716321, D5×C3⋊#11716322, …
maximal quotient ofC7×D5×D171, C3×C7×D5×D57, C7×D15×D57, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 150);