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C97×D165 #44544968

order32010
automorphism?
homologyAbelianization (H1) = C2×C97 · Schur multiplier (H2) = C1

Aliases

direct productC97×D165
unambiguous semidirect productC3⋊(C97×D55)
unambiguous semidirect productC5⋊(D33×C97)
unambiguous semidirect productC11⋊(D15×C97)

Splittings

Fitting, socle, HallC3×C5×C11×C97 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C97
HallC5×C11×C97 ⋊ D3
HallC3×C11×C97 ⋊ D5
HallC3×C5×C97 ⋊ D11
HallC11×C97 ⋊ D15
HallC5×C97 ⋊ D33
HallC3×C97 ⋊ D55
HallC5×C11 ⋊ D3×C97
HallC3×C11 ⋊ D5×C97
HallC3×C5 ⋊ D11×C97
SylowC11 ⋊ D15×C97
SylowC5 ⋊ D33×C97
SylowC3 ⋊ C97×D55

Subgroups

subgroupG/H
center, hypercenterC97D165
commutator, cosocle, hypocenterC3×C5×C11C2×C97
FrattiniC1G
Fitting, socleC3×C5×C11×C97C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16005

Conjugacy classes & character table

8148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 18);