Finite Group Databasebeta

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C107×D165 #47977229

order35310
automorphism?
homologyAbelianization (H1) = C2×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×D165
unambiguous semidirect productC3⋊(C107×D55)
unambiguous semidirect productC5⋊(D33×C107)
unambiguous semidirect productC11⋊(D15×C107)

Splittings

Fitting, socle, HallC3×C5×C11×C107 ⋊ C2
derived, HallC3×C5×C11 ⋊ C2×C107
HallC5×C11×C107 ⋊ D3
HallC3×C11×C107 ⋊ D5
HallC3×C5×C107 ⋊ D11
HallC11×C107 ⋊ D15
HallC5×C107 ⋊ D33
HallC3×C107 ⋊ D55
HallC5×C11 ⋊ D3×C107
HallC3×C11 ⋊ D5×C107
HallC3×C5 ⋊ D11×C107
SylowC11 ⋊ D15×C107
SylowC5 ⋊ D33×C107
SylowC3 ⋊ C107×D55

Subgroups

subgroupG/H
center, hypercenterC107D165
commutator, cosocle, hypocenterC3×C5×C11C2×C107
FrattiniC1G
Fitting, socleC3×C5×C11×C107C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C107

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17655

Conjugacy classes & character table

8988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35310, 16);