Finite Group Databasebeta

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C2×C3×D521⋊C5 #44530452

order31260
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D521⋊C5
unambiguous semidirect productD521⋊(C2×C3×C5)
unambiguous semidirect product(C2×D521)⋊(C3×C5)
unambiguous semidirect product(C521⋊C5)⋊(C22×C3)
unambiguous semidirect product(C2×C521⋊C5)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D521)⋊C5

Splittings

Fitting, socleC2×C3×C521 ⋊ C2×C5
derived, SylowC521 ⋊ C22×C3×C5
HallC3×C521⋊C5 ⋊ C22
HallC2×C3×D521 ⋊ C5
HallC521⋊C5 ⋊ C22×C3
HallC2×D521 ⋊ C3×C5
HallC3×C521 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D521⋊C5
commutator, cosocle, hypocenterC521C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C521C2×C5
LCSG ▷ C521
UCSC1 ◁ C2×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3126

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31260, 18);