Finite Group Databasebeta

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C2×C3×C5×D527 #44539399

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D527
unambiguous semidirect product(C2×C17)⋊(C3×C5×D31)

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC17×C31 ⋊ C22×C3×C5
HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C22×C3
HallC3×C17×C31 ⋊ C22×C5
HallC3×C5×C31 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ C2×C3×D17
HallC3×C31 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×C3×D31
HallC3×C17 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C3×C5×D17
SylowC17 ⋊ C2×C3×C5×D31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D527
commutator, cosocle, hypocenterC17×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C17×C31
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

7950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 156);