Finite Group Databasebeta

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C22×C13⋊C3×C41⋊C5 #44544341

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13⋊C3×C41⋊C5
unambiguous semidirect product(C22×C13⋊C3×C41)⋊C5

Splittings

Fitting, socle, HallC22×C13×C41 ⋊ C3×C5
derived, HallC13×C41 ⋊ C22×C3×C5
HallC22×C13×C41⋊C5 ⋊ C3
HallC22×C13⋊C3×C41 ⋊ C5
HallC13×C41⋊C5 ⋊ C22×C3
HallC13⋊C3×C41 ⋊ C22×C5
HallC22×C41 ⋊ C5×C13⋊C3
HallC22×C13 ⋊ C3×C41⋊C5
SylowC41 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C22×C3×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC22C13⋊C3×C41⋊C5
commutator, cosocle, hypocenterC13×C41C22×C3×C5
FrattiniC1G
Fitting, socleC22×C13×C41C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C22

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 69);