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C32×D1309 #37555654

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

Aliases

direct productC32×D1309
unambiguous semidirect productC11⋊(C32×D119)
unambiguous semidirect productC17⋊(C32×D77)

Splittings

Fitting, socle, HallC32×C7×C11×C17 ⋊ C2
derived, HallC7×C11×C17 ⋊ C2×C32
HallC32×C11×C17 ⋊ D7
HallC32×C7×C17 ⋊ D11
HallC32×C7×C11 ⋊ D17
HallC11×C17 ⋊ C32×D7
HallC32×C17 ⋊ D77
HallC7×C17 ⋊ C32×D11
HallC32×C11 ⋊ D119
HallC7×C11 ⋊ C32×D17
HallC32×C7 ⋊ D187
SylowC17 ⋊ C32×D77
SylowC11 ⋊ C32×D119
SylowC7 ⋊ C32×D187

Subgroups

subgroupG/H
center, hypercenterC32D1309
commutator, cosocle, hypocenterC7×C11×C17C2×C32
FrattiniC1G
Fitting, socleC32×C7×C11×C17C2
LCSG ▷ C7×C11×C17
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

5904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 48);