Finite Group Databasebeta

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D39×C23⋊C11 #34089418

order19734
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD39×C23⋊C11
unambiguous semidirect productC3⋊(D13×C23⋊C11)
unambiguous semidirect productC13⋊(D3×C23⋊C11)
unambiguous semidirect product(C23×D39)⋊C11

Splittings

Fitting, socle, derived, HallC3×C13×C23 ⋊ C2×C11
HallC3×C13×C23⋊C11 ⋊ C2
HallC13×C23⋊C11 ⋊ D3
HallC23×D39 ⋊ C11
HallC3×C23⋊C11 ⋊ D13
HallC13×C23 ⋊ D3×C11
HallC3×C23 ⋊ C11×D13
HallC3×C13 ⋊ C2×C23⋊C11
SylowC23 ⋊ C11×D39
SylowC13 ⋊ D3×C23⋊C11
SylowC3 ⋊ D13×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C23C2×C11
LCSG ▷ C3×C13×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 897

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 25);