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C59×(C13⋊C3)⋊D7 #44567287

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

Aliases

direct productC59×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(D7×C59)

Splittings

Fitting, socle, HallC7×C13×C59 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C59
HallC7×C13⋊C3×C59 ⋊ C2
HallC59×D91 ⋊ C3
HallC13⋊C3×C59 ⋊ D7
HallC13×C59 ⋊ C3×D7
HallC7×C59 ⋊ D13⋊C3
HallC7×C13⋊C3 ⋊ C2×C59
HallD91 ⋊ C3×C59
HallC13⋊C3 ⋊ D7×C59
SylowC13 ⋊ C3×D7×C59
SylowC7 ⋊ C59×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC59(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C2×C3×C59
FrattiniC1G
Fitting, socleC7×C13×C59C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5369

Conjugacy classes & character table

1711 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 41);