Finite Group Databasebeta

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C5×C7×C17×C13⋊C3 #37550939

order23205
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17×C13⋊C3
unambiguous semidirect productC13⋊(C3×C5×C7×C17)
unambiguous semidirect product(C5×C13)⋊(C3×C7×C17)
unambiguous semidirect product(C13×C17)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C13×C17)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C7×C17
HallC7×C13×C17 ⋊ C3×C5
HallC5×C13×C17 ⋊ C3×C7
HallC5×C7×C13 ⋊ C3×C17
HallC13×C17 ⋊ C3×C5×C7
HallC7×C13 ⋊ C3×C5×C17
HallC5×C13 ⋊ C3×C7×C17

Subgroups

subgroupG/H
center, hypercenterC5×C7×C17C13⋊C3
commutator, cosocle, hypocenterC13C3×C5×C7×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C3
LCSG ▷ C13
UCSC1 ◁ C5×C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

4165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23205, 2);