Finite Group Databasebeta

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C2×C3×C5×C17×C11⋊C5 #43242527

order28050
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C17 · Schur multiplier (H2) = C5

Aliases

direct productC2×C3×C5×C17×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C52×C17)
unambiguous semidirect product(C2×C3×C11)⋊(C52×C17)
unambiguous semidirect product(C2×C5×C11)⋊(C3×C5×C17)
unambiguous semidirect product(C2×C3×C5×C11)⋊(C5×C17)
unambiguous semidirect product(C2×C11×C17)⋊(C3×C52)
unambiguous semidirect product(C2×C3×C11×C17)⋊C52
unambiguous semidirect product(C2×C5×C11×C17)⋊(C3×C5)
unambiguous semidirect product(C2×C3×C5×C11×C17)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C52×C17
HallC2×C3×C11×C17 ⋊ C52
HallC3×C11×C17 ⋊ C2×C52
HallC2×C11×C17 ⋊ C3×C52
HallC11×C17 ⋊ C2×C3×C52
HallC2×C3×C11 ⋊ C52×C17
HallC3×C11 ⋊ C2×C52×C17
HallC2×C11 ⋊ C3×C52×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C52×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C17

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 52);