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C3×C5×(C17⋊D17)⋊C3 #39907233

order26010
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3×C17

Aliases

direct productC3×C5×(C17⋊D17)⋊C3
unambiguous semidirect product(C17⋊D17)⋊(C32×C5)
unambiguous semidirect product(C3×C17⋊D17)⋊(C3×C5)
unambiguous semidirect product(C5×C17⋊D17)⋊C32
unambiguous semidirect product(C3×C5×C17⋊D17)⋊C3

Splittings

Fitting, socleC3×C5×C172 ⋊ C2×C3
derived, SylowC172 ⋊ C2×C32×C5
HallC3×C5×C172⋊C3 ⋊ C2
HallC5×C17⋊D17 ⋊ C32
HallC3×C172⋊C3 ⋊ C2×C5
HallC5×C172 ⋊ C2×C32
HallC17⋊D17 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5(C17⋊D17)⋊C3
commutator, cosocle, hypocenterC172C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C172C2×C3
LCSG ▷ C172
UCSC1 ◁ C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 765

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26010, 47);