Finite Group Databasebeta

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C11×C17×C3⋊D21 #37555667

order23562
automorphism?
homologyAbelianization (H1) = C2×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC11×C17×C3⋊D21
unambiguous semidirect productC3⋊(C11×C17×D21)
unambiguous semidirect productC7⋊(C11×C17×C3⋊D3)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC32×C7 ⋊ C2×C11×C17
HallC32×C11×C17 ⋊ D7
HallC7×C11×C17 ⋊ C3⋊D3
HallC32×C7×C17 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C17
HallC32×C17 ⋊ C11×D7
HallC7×C17 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ D7×C17
HallC7×C11 ⋊ C17×C3⋊D3
SylowC32 ⋊ C11×D7×C17
SylowC7 ⋊ C11×C17×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC11×C17C3⋊D21
commutator, cosocle, hypocenterC32×C7C2×C11×C17
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C32×C7
UCSC1 ◁ C11×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

6171 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 61);