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C3×C5×D1271 #49185754

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1271

Splittings

Fitting, socle, HallC3×C5×C31×C41 ⋊ C2
derived, HallC31×C41 ⋊ C2×C3×C5
HallC5×C31×C41 ⋊ C2×C3
HallC3×C31×C41 ⋊ C2×C5
HallC3×C5×C41 ⋊ D31
HallC3×C5×C31 ⋊ D41
HallC5×C41 ⋊ C3×D31
HallC5×C31 ⋊ C3×D41
HallC3×C41 ⋊ C5×D31
HallC3×C31 ⋊ C5×D41
SylowC41 ⋊ C3×C5×D31
SylowC31 ⋊ C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC3×C5D1271
commutator, cosocle, hypocenterC31×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C31×C41C2
LCSG ▷ C31×C41
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19065

Conjugacy classes & character table

9555 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 17);