Finite Group Databasebeta

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C7×D5×D37⋊C3 #29509593

order15540
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×D37⋊C3
unambiguous semidirect productD37⋊(C3×C7×D5)
unambiguous semidirect product(D5×D37)⋊(C3×C7)
unambiguous semidirect product(C5×D37⋊C3)⋊(C2×C7)
unambiguous semidirect product(D5×C37⋊C3)⋊(C2×C7)
unambiguous semidirect product(C5⋊(D37⋊C3))⋊(C2×C7)

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C22×C3
derived, HallC5×C37 ⋊ C22×C3×C7
HallC7×D5×D37 ⋊ C3
HallC5×C7×C37⋊C3 ⋊ C22
HallC7×C37⋊C3 ⋊ C2×D5
HallD5×D37 ⋊ C3×C7
HallC5×C37⋊C3 ⋊ C22×C7
HallC7×C37 ⋊ C2×C3×D5
HallC37⋊C3 ⋊ C2×C7×D5
SylowC37 ⋊ C2×C3×C7×D5
HallC5×C7 ⋊ C2×D37⋊C3
SylowC5 ⋊ C2×C7×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D5×D37⋊C3
commutator, cosocle, hypocenterC5×C37C22×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C37C22×C3
LCSG ▷ C5×C37
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 95);