Finite Group Databasebeta

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C7×C23×D37⋊C3 #49088358

order35742
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×D37⋊C3
unambiguous semidirect productD37⋊(C3×C7×C23)
unambiguous semidirect product(C37⋊C3)⋊(C2×C7×C23)
unambiguous semidirect product(C23×D37)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C23×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C7×C23
HallC7×C23×C37⋊C3 ⋊ C2
HallC7×C23×D37 ⋊ C3
HallC23×C37⋊C3 ⋊ C2×C7
HallC23×D37 ⋊ C3×C7
HallC23×C37 ⋊ C2×C3×C7
HallC7×C37⋊C3 ⋊ C2×C23
HallC7×D37 ⋊ C3×C23
HallC7×C37 ⋊ C2×C3×C23
HallC37⋊C3 ⋊ C2×C7×C23
HallD37 ⋊ C3×C7×C23

Subgroups

subgroupG/H
center, hypercenterC7×C23D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C7×C23
FrattiniC1G
Fitting, socleC7×C23×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C7×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5957

Conjugacy classes & character table

1932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 21);