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C7×C23⋊(D37⋊C3) #49088366

order35742
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23⋊(D37⋊C3)
unambiguous semidirect productC23⋊(C7×D37⋊C3)
unambiguous semidirect product(C37⋊C3)⋊(C7×D23)
unambiguous semidirect productD851⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C23×C37 ⋊ C2×C3
derived, HallC23×C37 ⋊ C2×C3×C7
HallC7×C23×C37⋊C3 ⋊ C2
HallC7×D851 ⋊ C3
HallC23×C37⋊C3 ⋊ C2×C7
HallD851 ⋊ C3×C7
HallC7×C37⋊C3 ⋊ D23
HallC7×C37 ⋊ C3×D23
HallC7×C23 ⋊ D37⋊C3
HallC37⋊C3 ⋊ C7×D23
SylowC37 ⋊ C3×C7×D23
SylowC23 ⋊ C7×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C23⋊(D37⋊C3)
commutator, cosocle, hypocenterC23×C37C2×C3×C7
FrattiniC1G
Fitting, socleC7×C23×C37C2×C3
LCSG ▷ C23×C37
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 29);