Finite Group Databasebeta

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C3×C17×D231 #37555661

order23562
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×D231
unambiguous semidirect productC3⋊(C3×C17×D77)
unambiguous semidirect productC11⋊(C3×C17×D21)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derivedC3×C7×C11 ⋊ C2×C3×C17
HallC32×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ C3×D3
HallC32×C7×C17 ⋊ D11
HallC32×C7×C11 ⋊ C2×C17
HallC11×C17 ⋊ C3×D21
HallC32×C17 ⋊ D77
HallC7×C17 ⋊ C3×D33
HallC32×C11 ⋊ D7×C17
HallC7×C11 ⋊ C3×D3×C17
HallC32×C7 ⋊ C17×D11
SylowC11 ⋊ C3×C17×D21
SylowC32 ⋊ C17×D77
SylowC7 ⋊ C3×C17×D33

Subgroups

subgroupG/H
center, hypercenterC3×C17D231
commutator, cosocle, hypocenterC3×C7×C11C2×C3×C17
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

5967 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 55);