Finite Group Databasebeta

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D11×C23×C13⋊C3 #34089423

order19734
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productD11×C23×C13⋊C3
unambiguous semidirect productC11⋊(C2×C23×C13⋊C3)
unambiguous semidirect product(C13×D11)⋊(C3×C23)
unambiguous semidirect product(C13×D11×C23)⋊C3

Splittings

Fitting, socle, HallC11×C13×C23 ⋊ C2×C3
derived, HallC11×C13 ⋊ C2×C3×C23
HallC11×C23×C13⋊C3 ⋊ C2
HallC13×D11×C23 ⋊ C3
HallC11×C13⋊C3 ⋊ C2×C23
HallC13×C23 ⋊ C3×D11
HallC13×D11 ⋊ C3×C23
HallC11×C23 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×D11×C23
SylowC11 ⋊ C2×C23×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC23D11×C13⋊C3
commutator, cosocle, hypocenterC11×C13C2×C3×C23
FrattiniC1G
Fitting, socleC11×C13×C23C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3289

Conjugacy classes & character table

1127 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 30);