Finite Group Databasebeta

← Prev (#49112562) Next (#49112564) →

C2×C5×C11×C109⋊C3 #49112563

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

Aliases

direct productC2×C5×C11×C109⋊C3
unambiguous semidirect product(C2×C109)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C109)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C109)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C109 ⋊ C3
derived, SylowC109 ⋊ C2×C3×C5×C11
HallC5×C11×C109 ⋊ C2×C3
HallC2×C11×C109 ⋊ C3×C5
HallC11×C109 ⋊ C2×C3×C5
HallC2×C5×C109 ⋊ C3×C11
HallC5×C109 ⋊ C2×C3×C11
HallC2×C109 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C109⋊C3
commutator, cosocle, hypocenterC109C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C109C3
LCSG ▷ C109
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11990

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 3);