Finite Group Databasebeta

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C7×D5×D73⋊C3 #44501332

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×D73⋊C3
unambiguous semidirect productD73⋊(C3×C7×D5)
unambiguous semidirect product(D5×D73)⋊(C3×C7)
unambiguous semidirect product(C5×D73⋊C3)⋊(C2×C7)
unambiguous semidirect product(D5×C73⋊C3)⋊(C2×C7)
unambiguous semidirect product(C5⋊(D73⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C22×C3
derived, HallC5×C73 ⋊ C22×C3×C7
HallC7×D5×D73 ⋊ C3
HallC5×C7×C73⋊C3 ⋊ C22
HallC7×C73⋊C3 ⋊ C2×D5
HallD5×D73 ⋊ C3×C7
HallC5×C73⋊C3 ⋊ C22×C7
HallC7×C73 ⋊ C2×C3×D5
HallC73⋊C3 ⋊ C2×C7×D5
SylowC73 ⋊ C2×C3×C7×D5
HallC5×C7 ⋊ C2×D73⋊C3
SylowC5 ⋊ C2×C7×D73⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D5×D73⋊C3
commutator, cosocle, hypocenterC5×C73C22×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C73C22×C3
LCSG ▷ C5×C73
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 95);