Finite Group Databasebeta

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C5×C11⋊C5×C37⋊C3 #44479673

order30525
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×C37⋊C3
unambiguous semidirect productC11⋊(C52×C37⋊C3)
unambiguous semidirect productC37⋊(C3×C5×C11⋊C5)
unambiguous semidirect product(C5×C11)⋊(C5×C37⋊C3)
unambiguous semidirect product(C5×C37)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C37⋊C3)⋊C52
unambiguous semidirect product(C37×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C11×C37⋊C3)⋊C5
unambiguous semidirect product(C5×C37×C11⋊C5)⋊C3

Splittings

Fitting, socleC5×C11×C37 ⋊ C3×C5
derived, HallC11×C37 ⋊ C3×C52
HallC5×C37×C11⋊C5 ⋊ C3
HallC11×C37⋊C3 ⋊ C52
SylowC37 ⋊ C3×C5×C11⋊C5
SylowC11 ⋊ C52×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊C5×C37⋊C3
commutator, cosocle, hypocenterC11×C37C3×C52
FrattiniC1G
Fitting, socleC5×C11×C37C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30525, 6);