Finite Group Databasebeta

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D5×#13095536 #29509608

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

Aliases

direct productD5×#13095536

Splittings

Fitting, socle, derived, HallC5×C7×C37 ⋊ C22×C3
HallD5×D7×C37 ⋊ C3
HallC5×#11715912 ⋊ C22
Hall#11715912 ⋊ C2×D5
HallC7×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×AGL(1,𝔽7)
HallD5×D7 ⋊ C37⋊C3
SylowC37 ⋊ D5×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C37⋊C3
SylowC7 ⋊ C2×D5×C37⋊C3
SylowC5 ⋊ C2×#13095536

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C37C22×C3
LCSG ▷ C5×C7×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 110);