Finite Group Databasebeta

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C5×D2373 #37557538

order23730
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2373
unambiguous semidirect productC3⋊(C5×D791)
unambiguous semidirect productC7⋊(C5×D339)
unambiguous semidirect productC113⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C113 ⋊ C2
derived, HallC3×C7×C113 ⋊ C2×C5
HallC5×C7×C113 ⋊ D3
HallC3×C5×C113 ⋊ D7
HallC7×C113 ⋊ C5×D3
HallC5×C113 ⋊ D21
HallC3×C113 ⋊ C5×D7
SylowC113 ⋊ C5×D21
HallC3×C5×C7 ⋊ D113
HallC5×C7 ⋊ D339
HallC3×C7 ⋊ C5×D113
HallC3×C5 ⋊ D791
SylowC7 ⋊ C5×D339
SylowC3 ⋊ C5×D791

Subgroups

subgroupG/H
center, hypercenterC5D2373
commutator, cosocle, hypocenterC3×C7×C113C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C113C2
LCSG ▷ C3×C7×C113
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11865

Conjugacy classes & character table

5940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 14);