Finite Group Databasebeta

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C2×D5×C11×C49 #24924720

order10780
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C11×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C11×C49
unambiguous semidirect productC5⋊(C22×C11×C49)
unambiguous semidirect product(C2×C5)⋊(C2×C11×C49)

Splittings

FittingC2×C5×C11×C49 ⋊ C2
derived, SylowC5 ⋊ C22×C11×C49
HallC5×C11×C49 ⋊ C22
HallC5×C49 ⋊ C22×C11
HallC5×C11 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C11×C49D5
commutator, hypocenterC5C22×C11×C49
FrattiniC7C2×C7×D5×C11
FittingC2×C5×C11×C49C2
socleC2×C5×C7×C11C2×C7
prime radicalC2×C7×D5×C11C7
cosocleC5×C7C22×C7×C11
LCSG ▷ C5
UCSC1 ◁ C2×C11×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D5×C11×C49⋊C3, D3×D5×C11×C49, C2×C3×D5×C11×C49, …
maximal normal subgroup ofC2×D5×C11×C49⋊C3, C2×C3×D5×C11×C49
maximal quotient ofD3×D5×C11×C49, C2×C3×D5×C11×C49, C2×C11×D15×C49

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 33);