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C3×D85⋊D23 #37553309

order23460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D85⋊D23
unambiguous semidirect productD85⋊(C3×D23)
unambiguous semidirect productD115⋊(C3×D17)
unambiguous semidirect productD391⋊(C3×D5)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C22
derived, HallC5×C17×C23 ⋊ C22×C3
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ C2×C3×D5
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×C3×D17
HallC5×C17 ⋊ C2×C3×D23
HallC3×C23 ⋊ D5×D17
HallC3×C17 ⋊ D5×D23
SylowC23 ⋊ C3×D5×D17
SylowC17 ⋊ C3×D5×D23
HallC3×C5 ⋊ D17×D23
SylowC5 ⋊ C3×D17×D23

Subgroups

subgroupG/H
center, hypercenterC3D85⋊D23
commutator, cosocle, hypocenterC5×C17×C23C22×C3
FrattiniC1G
Fitting, socleC3×C5×C17×C23C22
LCSG ▷ C5×C17×C23
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

1572 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 36);