Finite Group Databasebeta

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C3×D17×D155 #44539351

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

Aliases

direct productC3×D17×D155
unambiguous semidirect product(C5×D17)⋊(C3×D31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C22
derived, HallC5×C17×C31 ⋊ C22×C3
HallC3×C17×C31 ⋊ C2×D5
HallC17×C31 ⋊ C2×C3×D5
HallC3×C5×C31 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ C2×C3×D17
HallC3×C31 ⋊ D5×D17
HallC5×C17 ⋊ C2×C3×D31
HallC3×C17 ⋊ C2×D155
SylowC31 ⋊ C3×D5×D17
SylowC17 ⋊ C2×C3×D155
HallC3×C5 ⋊ D17×D31
SylowC5 ⋊ C3×D17×D31

Subgroups

subgroupG/H
center, hypercenterC3D17×D155
commutator, cosocle, hypocenterC5×C17×C31C22×C3
FrattiniC1G
Fitting, socleC3×C5×C17×C31C22
LCSG ▷ C5×C17×C31
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

2370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 108);