Finite Group Databasebeta

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C11×D1065 #37552871

order23430
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1065
unambiguous semidirect productC3⋊(C11×D355)
unambiguous semidirect productC5⋊(C11×D213)
unambiguous semidirect productC71⋊(C11×D15)

Splittings

Fitting, socle, HallC3×C5×C11×C71 ⋊ C2
derived, HallC3×C5×C71 ⋊ C2×C11
HallC5×C11×C71 ⋊ D3
HallC3×C11×C71 ⋊ D5
HallC11×C71 ⋊ D15
HallC5×C71 ⋊ D3×C11
HallC3×C71 ⋊ D5×C11
HallC3×C5×C11 ⋊ D71
SylowC71 ⋊ C11×D15
HallC5×C11 ⋊ D213
HallC3×C11 ⋊ D355
HallC3×C5 ⋊ C11×D71
SylowC5 ⋊ C11×D213
SylowC3 ⋊ C11×D355

Subgroups

subgroupG/H
center, hypercenterC11D1065
commutator, cosocle, hypocenterC3×C5×C71C2×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C71C2
LCSG ▷ C3×C5×C71
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11715

Conjugacy classes & character table

5874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 20);