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C2×C31×D195 #37564012

order24180
automorphism?
homologyAbelianization (H1) = C22×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C31×D195
unambiguous semidirect product(C2×C3)⋊(C31×D65)
unambiguous semidirect product(C2×C5)⋊(C31×D39)
unambiguous semidirect product(C2×C13)⋊(D15×C31)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC3×C5×C13 ⋊ C22×C31
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C2×D3
HallC3×C13×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×D15
HallC5×C31 ⋊ C2×D39
HallC3×C31 ⋊ C2×D65
HallC5×C13 ⋊ C2×D3×C31
HallC3×C13 ⋊ C2×D5×C31
HallC3×C5 ⋊ C2×D13×C31
SylowC13 ⋊ C2×D15×C31
SylowC5 ⋊ C2×C31×D39
SylowC3 ⋊ C2×C31×D65

Subgroups

subgroupG/H
center, hypercenterC2×C31D195
commutator, cosocle, hypocenterC3×C5×C13C22×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

6138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 311);