Finite Group Databasebeta

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C3×C7×D517 #36343965

order21714
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D517
unambiguous semidirect productC11⋊(C3×C7×D47)
unambiguous semidirect productC47⋊(C3×C7×D11)

Splittings

Fitting, socle, HallC3×C7×C11×C47 ⋊ C2
derived, HallC11×C47 ⋊ C2×C3×C7
HallC7×C11×C47 ⋊ C2×C3
HallC3×C11×C47 ⋊ C2×C7
HallC3×C7×C47 ⋊ D11
HallC7×C47 ⋊ C3×D11
HallC3×C7×C11 ⋊ D47
HallC3×C47 ⋊ C7×D11
HallC7×C11 ⋊ C3×D47
SylowC47 ⋊ C3×C7×D11
HallC3×C11 ⋊ C7×D47
SylowC11 ⋊ C3×C7×D47

Subgroups

subgroupG/H
center, hypercenterC3×C7D517
commutator, cosocle, hypocenterC11×C47C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C47C2
LCSG ▷ C11×C47
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10857

Conjugacy classes & character table

5460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21714, 5);