Finite Group Databasebeta

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C11×D897 #34089408

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

Aliases

direct productC11×D897
unambiguous semidirect productC3⋊(C11×D299)
unambiguous semidirect productC13⋊(C11×D69)

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, HallC3×C13×C23 ⋊ C2×C11
HallC11×C13×C23 ⋊ D3
HallC3×C11×C23 ⋊ D13
HallC3×C11×C13 ⋊ D23
HallC13×C23 ⋊ D3×C11
HallC11×C23 ⋊ D39
HallC11×C13 ⋊ D69
HallC3×C23 ⋊ C11×D13
HallC3×C13 ⋊ C11×D23
HallC3×C11 ⋊ D299
SylowC23 ⋊ C11×D39
SylowC13 ⋊ C11×D69
SylowC3 ⋊ C11×D299

Subgroups

subgroupG/H
center, hypercenterC11D897
commutator, cosocle, hypocenterC3×C13×C23C2×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C3×C13×C23
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

4950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 15);