Finite Group Databasebeta

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C2×C5⋊#16838417 #50303457

order38220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#16838417
unambiguous semidirect product(C2×C5)⋊#16838417

Splittings

FittingC2×C5×C13×C49 ⋊ C2×C3
derived, HallC5×C13×C49 ⋊ C22×C3
HallC2×C13×D245 ⋊ C3
HallC5×#14274254 ⋊ C22
Hall#14274254 ⋊ C2×D5
HallC2×D245 ⋊ C13⋊C3
HallC13×C49 ⋊ C2×C3×D5
HallC5×C49 ⋊ C22×C13⋊C3
HallC5×C13 ⋊ C2×D49⋊C3
SylowC49 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×C5⋊(D49⋊C3)
SylowC5 ⋊ C2×#16838417

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16838417
commutator, cosocle, hypocenterC5×C13×C49C22×C3
FrattiniC7C2×C5⋊#10587720
FittingC2×C5×C13×C49C2×C3
socleC2×C5×C7×C13AGL(1,𝔽7)
LCSG ▷ C5×C13×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6370

Conjugacy classes & character table

1096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 143);