Finite Group Databasebeta

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C11×C41×D39 #47976010

order35178
automorphism?
homologyAbelianization (H1) = C2×C11×C41 · Schur multiplier (H2) = C1

Aliases

direct productC11×C41×D39
unambiguous semidirect productC3⋊(C11×D13×C41)
unambiguous semidirect productC13⋊(D3×C11×C41)

Splittings

Fitting, socle, HallC3×C11×C13×C41 ⋊ C2
derived, HallC3×C13 ⋊ C2×C11×C41
HallC11×C13×C41 ⋊ D3
HallC3×C13×C41 ⋊ C2×C11
HallC3×C11×C41 ⋊ D13
HallC13×C41 ⋊ D3×C11
HallC3×C11×C13 ⋊ C2×C41
HallC11×C13 ⋊ D3×C41
HallC3×C41 ⋊ C11×D13
HallC3×C11 ⋊ D13×C41
SylowC13 ⋊ D3×C11×C41
SylowC3 ⋊ C11×D13×C41

Subgroups

subgroupG/H
center, hypercenterC11×C41D39
commutator, cosocle, hypocenterC3×C13C2×C11×C41
FrattiniC1G
Fitting, socleC3×C11×C13×C41C2
LCSG ▷ C3×C13
UCSC1 ◁ C11×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17589

Conjugacy classes & character table

9471 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 12);