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C3×C17⋊(D61⋊C5) #44527449

order31110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17⋊(D61⋊C5)
unambiguous semidirect productC17⋊(C3×D61⋊C5)
unambiguous semidirect product(C3×D1037)⋊C5

Splittings

Fitting, socle, HallC3×C17×C61 ⋊ C2×C5
derived, HallC17×C61 ⋊ C2×C3×C5
HallC3×C17×C61⋊C5 ⋊ C2
HallC3×D1037 ⋊ C5
HallC17×C61⋊C5 ⋊ C2×C3
HallD1037 ⋊ C3×C5
HallC3×C61⋊C5 ⋊ D17
HallC61⋊C5 ⋊ C3×D17
HallC3×C61 ⋊ C5×D17
SylowC61 ⋊ C3×C5×D17
HallC3×C17 ⋊ D61⋊C5
SylowC17 ⋊ C3×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C17⋊(D61⋊C5)
commutator, cosocle, hypocenterC17×C61C2×C3×C5
FrattiniC1G
Fitting, socleC3×C17×C61C2×C5
LCSG ▷ C17×C61
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3111

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 22);