Finite Group Databasebeta

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C2×C5⋊#13095535 #29509641

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

Aliases

direct productC2×C5⋊#13095535
unambiguous semidirect product(C2×C5)⋊#13095535

Splittings

Fitting, socleC2×C5×C7×C37 ⋊ C2×C3
derived, HallC5×C7×C37 ⋊ C22×C3
HallC2×C37×D35 ⋊ C3
HallC5×#11715913 ⋊ C22
Hall#11715913 ⋊ C2×D5
HallC7×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×AGL(1,𝔽7)
HallC2×D35 ⋊ C37⋊C3
SylowC37 ⋊ C2×C5⋊AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C37⋊C3
SylowC7 ⋊ C2×D5×C37⋊C3
SylowC5 ⋊ C2×#13095535

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#13095535
commutator, cosocle, hypocenterC5×C7×C37C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C37C2×C3
LCSG ▷ C5×C7×C37
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2590

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15540, 143);