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C17×(D61⋊C3)⋊C5 #44527461

order31110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(D61⋊C3)⋊C5
unambiguous semidirect product(D61⋊C3)⋊(C5×C17)
unambiguous semidirect product(D61⋊C5)⋊(C3×C17)
unambiguous semidirect product((C61⋊C3)⋊C5)⋊(C2×C17)
unambiguous semidirect product(C17×D61⋊C3)⋊C5
unambiguous semidirect product(C17×D61⋊C5)⋊C3

Splittings

Fitting, socle, HallC17×C61 ⋊ C2×C3×C5
derived, SylowC61 ⋊ C2×C3×C5×C17
HallC17×(C61⋊C3)⋊C5 ⋊ C2
HallC17×D61⋊C5 ⋊ C3
HallC17×D61⋊C3 ⋊ C5
HallC17×C61⋊C5 ⋊ C2×C3
HallC17×C61⋊C3 ⋊ C2×C5
HallC17×D61 ⋊ C3×C5
Hall(C61⋊C3)⋊C5 ⋊ C2×C17
HallD61⋊C5 ⋊ C3×C17
HallD61⋊C3 ⋊ C5×C17
HallC61⋊C5 ⋊ C2×C3×C17
HallC61⋊C3 ⋊ C2×C5×C17
HallD61 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC17(D61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C17
FrattiniC1G
Fitting, socleC17×C61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1037

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 34);