Finite Group Databasebeta

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C11×C13×D123 #47976009

order35178
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×D123
unambiguous semidirect productC3⋊(C11×C13×D41)
unambiguous semidirect productC41⋊(D3×C11×C13)

Splittings

Fitting, socle, HallC3×C11×C13×C41 ⋊ C2
derived, HallC3×C41 ⋊ C2×C11×C13
HallC11×C13×C41 ⋊ D3
HallC3×C13×C41 ⋊ C2×C11
HallC3×C11×C41 ⋊ C2×C13
HallC13×C41 ⋊ D3×C11
HallC11×C41 ⋊ D3×C13
HallC3×C11×C13 ⋊ D41
SylowC41 ⋊ D3×C11×C13
HallC3×C13 ⋊ C11×D41
HallC3×C11 ⋊ C13×D41
SylowC3 ⋊ C11×C13×D41

Subgroups

subgroupG/H
center, hypercenterC11×C13D123
commutator, cosocle, hypocenterC3×C41C2×C11×C13
FrattiniC1G
Fitting, socleC3×C11×C13×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17589

Conjugacy classes & character table

9009 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 11);