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C3×C49×C11⋊C5 #22549110

order8085
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×C11⋊C5
unambiguous semidirect productC11⋊(C3×C5×C49)
unambiguous semidirect product(C3×C11)⋊(C5×C49)
unambiguous semidirect product(C3×C11×C49)⋊C5

Splittings

Fitting, HallC3×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C3×C5×C49
HallC11×C49 ⋊ C3×C5
HallC3×C11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49C11⋊C5
commutator, hypocenterC11C3×C5×C49
FrattiniC7C3×C7×C11⋊C5
FittingC3×C11×C49C5
socleC3×C7×C11C5×C7
LCSG ▷ C11
UCSC1 ◁ C3×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1029 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C49×C11⋊C5, C3×C49×AGL(1,𝔽11), C3×C11⋊C5×D49, …
maximal normal subgroup ofC2×C3×C49×C11⋊C5, C3×C49×AGL(1,𝔽11), C3×C11⋊C5×D49, …
maximal quotient ofC2×C3×C49×C11⋊C5, C9×C49×C11⋊C5, C32×C49×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8085, 3);