Finite Group Databasebeta

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C32×C7×D187 #37555650

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

Aliases

direct productC32×C7×D187
unambiguous semidirect productC11⋊(C32×C7×D17)
unambiguous semidirect productC17⋊(C32×C7×D11)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC11×C17 ⋊ C2×C32×C7
HallC32×C11×C17 ⋊ C2×C7
HallC7×C11×C17 ⋊ C2×C32
HallC32×C7×C17 ⋊ D11
HallC32×C7×C11 ⋊ D17
HallC32×C17 ⋊ C7×D11
HallC7×C17 ⋊ C32×D11
HallC32×C11 ⋊ C7×D17
HallC7×C11 ⋊ C32×D17
SylowC17 ⋊ C32×C7×D11
SylowC11 ⋊ C32×C7×D17

Subgroups

subgroupG/H
center, hypercenterC32×C7D187
commutator, cosocle, hypocenterC11×C17C2×C32×C7
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C11×C17
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5985 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 44);