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C2×C11×#13131975 #49146297

order36894
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×#13131975

Splittings

Fitting, socle, HallC2×C11×C13×C43 ⋊ C3
derived, HallC13×C43 ⋊ C2×C3×C11
HallC11×C13×C43 ⋊ C2×C3
HallC2×C13×C43 ⋊ C3×C11
HallC2×C11×C43 ⋊ C13⋊C3
HallC11×C43 ⋊ C2×C13⋊C3
HallC2×C11×C13 ⋊ C43⋊C3
HallC11×C13 ⋊ C2×C43⋊C3
HallC2×C43 ⋊ C11×C13⋊C3
SylowC43 ⋊ C2×C11×C13⋊C3
HallC2×C13 ⋊ C11×C43⋊C3
SylowC13 ⋊ C2×C11×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#13131975
commutator, cosocle, hypocenterC13×C43C2×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C13×C43C3
LCSG ▷ C13×C43
UCSC1 ◁ C2×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12298

Conjugacy classes & character table

4158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36894, 5);