Finite Group Databasebeta

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C5×C17×C11⋊C5 #17989727

order4675
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52×C17 · Schur multiplier (H2) = C5

Aliases

direct productC5×C17×C11⋊C5
unambiguous semidirect productC11⋊(C52×C17)
unambiguous semidirect product(C5×C11)⋊(C5×C17)
unambiguous semidirect product(C11×C17)⋊C52
unambiguous semidirect product(C5×C11×C17)⋊C5

Splittings

Fitting, socleC5×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C52×C17
HallC11×C17 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C17C11⋊C5
commutator, cosocle, hypocenterC11C52×C17
FrattiniC1G
Fitting, socleC5×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 935

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C5×C17×C11⋊C5, C5×C7×C17×C11⋊C5
maximal normal subgroup ofC3×C5×C17×C11⋊C5, C5×C7×C17×C11⋊C5
maximal quotient ofC3×C5×C17×C11⋊C5, C5×C7×C17×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4675, 4);