Finite Group Databasebeta

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C2×C3×C5×D533 #44544488

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

Aliases

direct productC2×C3×C5×D533

Splittings

Fitting, socleC2×C3×C5×C13×C41 ⋊ C2
derived, HallC13×C41 ⋊ C22×C3×C5
HallC3×C5×C13×C41 ⋊ C22
HallC5×C13×C41 ⋊ C22×C3
HallC3×C13×C41 ⋊ C22×C5
HallC3×C5×C41 ⋊ C2×D13
HallC5×C41 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ C2×C3×C5×D13
HallC3×C13 ⋊ C2×C5×D41
SylowC13 ⋊ C2×C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D533
commutator, cosocle, hypocenterC13×C41C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C41C2
LCSG ▷ C13×C41
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15990

Conjugacy classes & character table

8040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 216);