Finite Group Databasebeta

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C2×C52⋊#10625202 #49150310

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC2×C52⋊#10625202
unambiguous semidirect product(C2×C52)⋊#10625202

Splittings

Fitting, socle, HallC2×C52×C13×C19 ⋊ C3
derived, HallC52×C13×C19 ⋊ C2×C3
HallC2×C52×C19 ⋊ C13⋊C3
HallC2×C52×C13 ⋊ C19⋊C3
HallC2×C13×C19 ⋊ C52⋊C3
HallC52×C19 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C2×C19⋊C3
HallC13×C19 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ #10625202
HallC2×C19 ⋊ C13⋊(C52⋊C3)
HallC2×C13 ⋊ C19⋊(C52⋊C3)
SylowC52 ⋊ C2×#10625202
SylowC19 ⋊ C2×C13⋊(C52⋊C3)
SylowC13 ⋊ C2×C19⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C52⋊#10625202
commutator, cosocle, hypocenterC52×C13×C19C2×C3
FrattiniC1G
Fitting, socleC2×C52×C13×C19C3
LCSG ▷ C52×C13×C19
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7410

Conjugacy classes & character table

4122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 136);