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C13×(C43⋊C3)⋊D7 #37553505

order23478
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C43⋊C3)⋊D7
unambiguous semidirect product(C43⋊C3)⋊(C13×D7)

Splittings

Fitting, socle, HallC7×C13×C43 ⋊ C2×C3
derived, HallC7×C43 ⋊ C2×C3×C13
HallC7×C13×C43⋊C3 ⋊ C2
HallC13×D301 ⋊ C3
HallC13×C43⋊C3 ⋊ D7
HallC7×C43⋊C3 ⋊ C2×C13
HallD301 ⋊ C3×C13
HallC13×C43 ⋊ C3×D7
HallC43⋊C3 ⋊ C13×D7
HallC7×C13 ⋊ D43⋊C3
SylowC43 ⋊ C3×C13×D7
SylowC7 ⋊ C13×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC13(C43⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C43C2×C3×C13
FrattiniC1G
Fitting, socleC7×C13×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3913

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 94);