Finite Group Databasebeta

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C3×C71×D55 #37552864

order23430
automorphism?
homologyAbelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1

Aliases

direct productC3×C71×D55
unambiguous semidirect productC5⋊(C3×D11×C71)
unambiguous semidirect productC11⋊(C3×D5×C71)

Splittings

Fitting, socle, HallC3×C5×C11×C71 ⋊ C2
derived, HallC5×C11 ⋊ C2×C3×C71
HallC5×C11×C71 ⋊ C2×C3
HallC3×C11×C71 ⋊ D5
HallC3×C5×C71 ⋊ D11
HallC11×C71 ⋊ C3×D5
HallC5×C71 ⋊ C3×D11
HallC3×C5×C11 ⋊ C2×C71
HallC3×C11 ⋊ D5×C71
HallC3×C5 ⋊ D11×C71
SylowC11 ⋊ C3×D5×C71
SylowC5 ⋊ C3×D11×C71

Subgroups

subgroupG/H
center, hypercenterC3×C71D55
commutator, cosocle, hypocenterC5×C11C2×C3×C71
FrattiniC1G
Fitting, socleC3×C5×C11×C71C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11715

Conjugacy classes & character table

6177 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 13);