Finite Group Databasebeta

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C3×C11×D355 #37552863

order23430
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D355
unambiguous semidirect productC5⋊(C3×C11×D71)
unambiguous semidirect productC71⋊(C3×D5×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C71 ⋊ C2
derived, HallC5×C71 ⋊ C2×C3×C11
HallC5×C11×C71 ⋊ C2×C3
HallC3×C11×C71 ⋊ D5
HallC3×C5×C71 ⋊ C2×C11
HallC11×C71 ⋊ C3×D5
HallC3×C71 ⋊ D5×C11
HallC3×C5×C11 ⋊ D71
SylowC71 ⋊ C3×D5×C11
HallC5×C11 ⋊ C3×D71
HallC3×C5 ⋊ C11×D71
SylowC5 ⋊ C3×C11×D71

Subgroups

subgroupG/H
center, hypercenterC3×C11D355
commutator, cosocle, hypocenterC5×C71C2×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C71C2
LCSG ▷ C5×C71
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11715

Conjugacy classes & character table

5907 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 12);