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C43×D273 #37553444

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

Aliases

direct productC43×D273
unambiguous semidirect productC3⋊(C43×D91)
unambiguous semidirect productC7⋊(C43×D39)
unambiguous semidirect productC13⋊(D21×C43)

Splittings

Fitting, socle, HallC3×C7×C13×C43 ⋊ C2
derived, HallC3×C7×C13 ⋊ C2×C43
HallC7×C13×C43 ⋊ D3
HallC3×C13×C43 ⋊ D7
HallC3×C7×C43 ⋊ D13
HallC13×C43 ⋊ D21
HallC7×C43 ⋊ D39
HallC3×C43 ⋊ D91
HallC7×C13 ⋊ D3×C43
HallC3×C13 ⋊ D7×C43
HallC3×C7 ⋊ D13×C43
SylowC13 ⋊ D21×C43
SylowC7 ⋊ C43×D39
SylowC3 ⋊ C43×D91

Subgroups

subgroupG/H
center, hypercenterC43D273
commutator, cosocle, hypocenterC3×C7×C13C2×C43
FrattiniC1G
Fitting, socleC3×C7×C13×C43C2
LCSG ▷ C3×C7×C13
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11739

Conjugacy classes & character table

5934 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 33);