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C22×C49×C11⋊C5 #24924705

order10780
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC22×C49×C11⋊C5
unambiguous semidirect product(C22×C11)⋊(C5×C49)
unambiguous semidirect product(C22×C11×C49)⋊C5

Splittings

Fitting, HallC22×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C22×C5×C49
HallC11×C49 ⋊ C22×C5
HallC22×C11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC22×C49C11⋊C5
commutator, hypocenterC11C22×C5×C49
FrattiniC7C22×C7×C11⋊C5
FittingC22×C11×C49C5
socleC22×C7×C11C5×C7
prime radicalC22×C7×C11⋊C5C7
cosocleC7×C11C22×C5×C7
LCSG ▷ C11
UCSC1 ◁ C22×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C11⋊C5×C49⋊C3, A4×C49×C11⋊C5, C11⋊C5×C22⋊(C49⋊C3), …
maximal normal subgroup ofC22×C11⋊C5×C49⋊C3, A4×C49×C11⋊C5, C11⋊C5×C22⋊(C49⋊C3), …
maximal quotient ofC2×D3×C49×C11⋊C5, C22×C3×C49×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 18);