Finite Group Databasebeta

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C5×C7×C17×C11⋊C5 #45658562

order32725
automorphism?
homologyAbelianization (H1) = C52×C7×C17 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C17×C11⋊C5
unambiguous semidirect productC11⋊(C52×C7×C17)
unambiguous semidirect product(C5×C11)⋊(C5×C7×C17)
unambiguous semidirect product(C7×C11)⋊(C52×C17)
unambiguous semidirect product(C11×C17)⋊(C52×C7)
unambiguous semidirect product(C5×C7×C11)⋊(C5×C17)
unambiguous semidirect product(C5×C11×C17)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C17)⋊C52
unambiguous semidirect product(C5×C7×C11×C17)⋊C5

Splittings

Fitting, socleC5×C7×C11×C17 ⋊ C5
derived, SylowC11 ⋊ C52×C7×C17
HallC7×C11×C17 ⋊ C52
HallC11×C17 ⋊ C52×C7
HallC7×C11 ⋊ C52×C17

Subgroups

subgroupG/H
center, hypercenterC5×C7×C17C11⋊C5
commutator, cosocle, hypocenterC11C52×C7×C17
FrattiniC1G
Fitting, socleC5×C7×C11×C17C5
LCSG ▷ C11
UCSC1 ◁ C5×C7×C17

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

4165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32725, 4);