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C7×D2553 #49088353

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

Aliases

direct productC7×D2553
unambiguous semidirect productC3⋊(C7×D851)
unambiguous semidirect productC23⋊(C7×D111)
unambiguous semidirect productC37⋊(C7×D69)

Splittings

Fitting, socle, HallC3×C7×C23×C37 ⋊ C2
derived, HallC3×C23×C37 ⋊ C2×C7
HallC7×C23×C37 ⋊ D3
HallC23×C37 ⋊ D3×C7
HallC3×C7×C37 ⋊ D23
HallC3×C7×C23 ⋊ D37
HallC7×C37 ⋊ D69
HallC7×C23 ⋊ D111
HallC3×C37 ⋊ C7×D23
HallC3×C23 ⋊ C7×D37
SylowC37 ⋊ C7×D69
SylowC23 ⋊ C7×D111
HallC3×C7 ⋊ D851
SylowC3 ⋊ C7×D851

Subgroups

subgroupG/H
center, hypercenterC7D2553
commutator, cosocle, hypocenterC3×C23×C37C2×C7
FrattiniC1G
Fitting, socleC3×C7×C23×C37C2
LCSG ▷ C3×C23×C37
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17871

Conjugacy classes & character table

8946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35742, 16);