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C5×D2397 #37561794

order23970
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2397
unambiguous semidirect productC3⋊(C5×D799)
unambiguous semidirect productC17⋊(C5×D141)
unambiguous semidirect productC47⋊(C5×D51)

Splittings

Fitting, socle, HallC3×C5×C17×C47 ⋊ C2
derived, HallC3×C17×C47 ⋊ C2×C5
HallC5×C17×C47 ⋊ D3
HallC17×C47 ⋊ C5×D3
HallC3×C5×C47 ⋊ D17
HallC3×C5×C17 ⋊ D47
HallC5×C47 ⋊ D51
HallC3×C47 ⋊ C5×D17
HallC5×C17 ⋊ D141
HallC3×C17 ⋊ C5×D47
SylowC47 ⋊ C5×D51
SylowC17 ⋊ C5×D141
HallC3×C5 ⋊ D799
SylowC3 ⋊ C5×D799

Subgroups

subgroupG/H
center, hypercenterC5D2397
commutator, cosocle, hypocenterC3×C17×C47C2×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C47C2
LCSG ▷ C3×C17×C47
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11985

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23970, 12);