Finite Group Databasebeta

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C3×C7×D561 #37555658

order23562
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D561
unambiguous semidirect productC3⋊(C3×C7×D187)
unambiguous semidirect productC11⋊(C3×C7×D51)
unambiguous semidirect productC17⋊(C3×C7×D33)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derivedC3×C11×C17 ⋊ C2×C3×C7
HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C3×D3
HallC32×C7×C17 ⋊ D11
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C3×D3×C7
HallC32×C17 ⋊ C7×D11
HallC7×C17 ⋊ C3×D33
HallC32×C11 ⋊ C7×D17
HallC7×C11 ⋊ C3×D51
HallC32×C7 ⋊ D187
SylowC17 ⋊ C3×C7×D33
SylowC11 ⋊ C3×C7×D51
SylowC32 ⋊ C7×D187

Subgroups

subgroupG/H
center, hypercenterC3×C7D561
commutator, cosocle, hypocenterC3×C11×C17C2×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

5922 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 52);