Finite Group Databasebeta

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C3×C5×C11×D109 #49112565

order35970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D109

Splittings

Fitting, socle, HallC3×C5×C11×C109 ⋊ C2
derived, SylowC109 ⋊ C2×C3×C5×C11
HallC5×C11×C109 ⋊ C2×C3
HallC3×C11×C109 ⋊ C2×C5
HallC3×C5×C109 ⋊ C2×C11
HallC11×C109 ⋊ C2×C3×C5
HallC5×C109 ⋊ C2×C3×C11
HallC3×C109 ⋊ C2×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D109
commutator, cosocle, hypocenterC109C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C109C2
LCSG ▷ C109
UCSC1 ◁ C3×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17985

Conjugacy classes & character table

9240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 5);