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C43×(C13⋊C3)⋊D7 #37553519

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×(C13⋊C3)⋊D7
unambiguous semidirect product(C13⋊C3)⋊(D7×C43)

Splittings

Fitting, socle, HallC7×C13×C43 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C43
HallC7×C13⋊C3×C43 ⋊ C2
HallC43×D91 ⋊ C3
HallC13⋊C3×C43 ⋊ D7
HallC13×C43 ⋊ C3×D7
HallC7×C43 ⋊ D13⋊C3
HallC7×C13⋊C3 ⋊ C2×C43
HallD91 ⋊ C3×C43
HallC13⋊C3 ⋊ D7×C43
SylowC13 ⋊ C3×D7×C43
SylowC7 ⋊ C43×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC43(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C13C2×C3×C43
FrattiniC1G
Fitting, socleC7×C13×C43C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3913

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 108);