Finite Group Databasebeta

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C3×C7×C11×D51 #37555656

order23562
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D51
unambiguous semidirect productC3⋊(C3×C7×C11×D17)
unambiguous semidirect productC17⋊(C3×D3×C7×C11)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derivedC3×C17 ⋊ C2×C3×C7×C11
HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C3×D3
HallC32×C7×C17 ⋊ C2×C11
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C3×D3×C7
HallC32×C17 ⋊ C2×C7×C11
HallC7×C17 ⋊ C3×D3×C11
HallC32×C11 ⋊ C7×D17
HallC32×C7 ⋊ C11×D17
SylowC17 ⋊ C3×D3×C7×C11
SylowC32 ⋊ C7×C11×D17

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D51
commutator, cosocle, hypocenterC3×C17C2×C3×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C3×C17
UCSC1 ◁ C3×C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

6237 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 50);