Finite Group Databasebeta

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C7×C11×C17×C3⋊D3 #37555663

order23562
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC7×C11×C17×C3⋊D3
unambiguous semidirect productC3⋊(D3×C7×C11×C17)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, SylowC32 ⋊ C2×C7×C11×C17
HallC32×C11×C17 ⋊ C2×C7
HallC32×C7×C17 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C17
HallC32×C17 ⋊ C2×C7×C11
HallC32×C11 ⋊ C2×C7×C17
HallC32×C7 ⋊ C2×C11×C17

Subgroups

subgroupG/H
center, hypercenterC7×C11×C17C3⋊D3
commutator, cosocle, hypocenterC32C2×C7×C11×C17
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C32
UCSC1 ◁ C7×C11×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 57);