Finite Group Databasebeta

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C7×C59×D13⋊C3 #44567271

order32214
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C59 · Schur multiplier (H2) = C1

Aliases

direct productC7×C59×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×C59)
unambiguous semidirect product(C13⋊C3)⋊(C2×C7×C59)
unambiguous semidirect product(D13×C59)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C59 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C7×C59
HallC7×C13⋊C3×C59 ⋊ C2
HallC7×D13×C59 ⋊ C3
HallC13⋊C3×C59 ⋊ C2×C7
HallD13×C59 ⋊ C3×C7
HallC13×C59 ⋊ C2×C3×C7
HallC7×C13⋊C3 ⋊ C2×C59
HallC7×D13 ⋊ C3×C59
HallC7×C13 ⋊ C2×C3×C59
HallC13⋊C3 ⋊ C2×C7×C59
HallD13 ⋊ C3×C7×C59

Subgroups

subgroupG/H
center, hypercenterC7×C59D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C7×C59
FrattiniC1G
Fitting, socleC7×C13×C59C2×C3
LCSG ▷ C13
UCSC1 ◁ C7×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5369

Conjugacy classes & character table

3304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 25);