Finite Group Databasebeta

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C11×D15×C109 #49112576

order35970
automorphism?
homologyAbelianization (H1) = C2×C11×C109 · Schur multiplier (H2) = C1

Aliases

direct productC11×D15×C109
unambiguous semidirect productC3⋊(D5×C11×C109)
unambiguous semidirect productC5⋊(D3×C11×C109)

Splittings

Fitting, socle, HallC3×C5×C11×C109 ⋊ C2
derived, HallC3×C5 ⋊ C2×C11×C109
HallC5×C11×C109 ⋊ D3
HallC3×C11×C109 ⋊ D5
HallC3×C5×C109 ⋊ C2×C11
HallC5×C109 ⋊ D3×C11
HallC3×C109 ⋊ D5×C11
HallC3×C5×C11 ⋊ C2×C109
HallC5×C11 ⋊ D3×C109
HallC3×C11 ⋊ D5×C109
SylowC5 ⋊ D3×C11×C109
SylowC3 ⋊ D5×C11×C109

Subgroups

subgroupG/H
center, hypercenterC11×C109D15
commutator, cosocle, hypocenterC3×C5C2×C11×C109
FrattiniC1G
Fitting, socleC3×C5×C11×C109C2
LCSG ▷ C3×C5
UCSC1 ◁ C11×C109

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17985

Conjugacy classes & character table

10791 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 16);