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C23×(C37⋊C3)⋊D7 #49088374

order35742
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C37⋊C3)⋊D7
unambiguous semidirect product(C37⋊C3)⋊(D7×C23)

Splittings

Fitting, socle, HallC7×C23×C37 ⋊ C2×C3
derived, HallC7×C37 ⋊ C2×C3×C23
HallC7×C23×C37⋊C3 ⋊ C2
HallC23×D259 ⋊ C3
HallC23×C37⋊C3 ⋊ D7
HallC23×C37 ⋊ C3×D7
HallC7×C37⋊C3 ⋊ C2×C23
HallD259 ⋊ C3×C23
HallC7×C23 ⋊ D37⋊C3
HallC37⋊C3 ⋊ D7×C23
SylowC37 ⋊ C3×D7×C23
SylowC7 ⋊ C23×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC23(C37⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C37C2×C3×C23
FrattiniC1G
Fitting, socleC7×C23×C37C2×C3
LCSG ▷ C7×C37
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 37);