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C11×D1677 #49146308

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

Aliases

direct productC11×D1677
unambiguous semidirect productC3⋊(C11×D559)
unambiguous semidirect productC13⋊(C11×D129)
unambiguous semidirect productC43⋊(C11×D39)

Splittings

Fitting, socle, HallC3×C11×C13×C43 ⋊ C2
derived, HallC3×C13×C43 ⋊ C2×C11
HallC11×C13×C43 ⋊ D3
HallC3×C11×C43 ⋊ D13
HallC13×C43 ⋊ D3×C11
HallC11×C43 ⋊ D39
HallC3×C11×C13 ⋊ D43
HallC11×C13 ⋊ D129
HallC3×C43 ⋊ C11×D13
SylowC43 ⋊ C11×D39
HallC3×C13 ⋊ C11×D43
HallC3×C11 ⋊ D559
SylowC13 ⋊ C11×D129
SylowC3 ⋊ C11×D559

Subgroups

subgroupG/H
center, hypercenterC11D1677
commutator, cosocle, hypocenterC3×C13×C43C2×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C43C2
LCSG ▷ C3×C13×C43
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18447

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(36894, 16);