Finite Group Databasebeta

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C3×C7×D759 #44541815

order31878
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D759
unambiguous semidirect productC3⋊(C3×C7×D253)
unambiguous semidirect productC11⋊(C3×C7×D69)
unambiguous semidirect productC23⋊(C3×C7×D33)

Splittings

Fitting, socle, HallC32×C7×C11×C23 ⋊ C2
derivedC3×C11×C23 ⋊ C2×C3×C7
HallC32×C11×C23 ⋊ C2×C7
HallC7×C11×C23 ⋊ C3×D3
HallC32×C7×C23 ⋊ D11
HallC32×C7×C11 ⋊ D23
HallC11×C23 ⋊ C3×D3×C7
HallC32×C23 ⋊ C7×D11
HallC7×C23 ⋊ C3×D33
HallC32×C11 ⋊ C7×D23
HallC7×C11 ⋊ C3×D69
HallC32×C7 ⋊ D253
SylowC23 ⋊ C3×C7×D33
SylowC11 ⋊ C3×C7×D69
SylowC32 ⋊ C7×D253

Subgroups

subgroupG/H
center, hypercenterC3×C7D759
commutator, cosocle, hypocenterC3×C11×C23C2×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C23C2
LCSG ▷ C3×C11×C23
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10626

Conjugacy classes & character table

8001 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31878, 84);