Finite Group Databasebeta

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C32×C7×C11×D17 #37555648

order23562
automorphism?
homologyAbelianization (H1) = C2×C32×C7×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×C11×D17
unambiguous semidirect productC17⋊(C2×C32×C7×C11)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C32×C7×C11
HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C2×C32
HallC32×C7×C17 ⋊ C2×C11
HallC11×C17 ⋊ C2×C32×C7
HallC32×C17 ⋊ C2×C7×C11
HallC7×C17 ⋊ C2×C32×C11

Subgroups

subgroupG/H
center, hypercenterC32×C7×C11D17
commutator, cosocle, hypocenterC17C2×C32×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C32×C7×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

6930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 42);