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C2×C3×C11⋊C5×C109 #49112562

order35970
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C109 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC2×C3×C11×C109 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C109
HallC3×C11×C109 ⋊ C2×C5
HallC2×C11×C109 ⋊ C3×C5
HallC11×C109 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C109
HallC3×C11 ⋊ C2×C5×C109
HallC2×C11 ⋊ C3×C5×C109

Subgroups

subgroupG/H
center, hypercenterC2×C3×C109C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C109
FrattiniC1G
Fitting, socleC2×C3×C11×C109C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C109

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7194

Conjugacy classes & character table

4578 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35970, 2);