Finite Group Databasebeta

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C3×C11×D299 #34089400

order19734
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D299

Splittings

Fitting, socle, HallC3×C11×C13×C23 ⋊ C2
derived, HallC13×C23 ⋊ C2×C3×C11
HallC11×C13×C23 ⋊ C2×C3
HallC3×C13×C23 ⋊ C2×C11
HallC3×C11×C23 ⋊ D13
HallC3×C11×C13 ⋊ D23
HallC11×C23 ⋊ C3×D13
HallC11×C13 ⋊ C3×D23
HallC3×C23 ⋊ C11×D13
HallC3×C13 ⋊ C11×D23
SylowC23 ⋊ C3×C11×D13
SylowC13 ⋊ C3×C11×D23

Subgroups

subgroupG/H
center, hypercenterC3×C11D299
commutator, cosocle, hypocenterC13×C23C2×C3×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C23C2
LCSG ▷ C13×C23
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9867

Conjugacy classes & character table

4983 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 7);