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C49×Dic11⋊C5 #24924689

order10780
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C49)
unambiguous semidirect product(C11⋊C5)⋊(C4×C49)
unambiguous semidirect product(Dic11×C49)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C49
HallC49×C11⋊C5 ⋊ C4
HallDic11×C49 ⋊ C5
HallC11×C49 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C49
HallDic11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C49
FrattiniC2×C7C7×AGL(1,𝔽11)
FittingC2×C11×C49C2×C5
socle, cosocleC2×C7×C11C2×C5×C7
prime radicalC2×C7×C11⋊C5C2×C7
LCSG ▷ C11
UCSC1 ◁ C2×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C49×Dic11⋊C5, C49×C3⋊(Dic11⋊C5), C49⋊C3×Dic11⋊C5
maximal normal subgroup ofC3×C49×Dic11⋊C5, C49⋊C3×Dic11⋊C5
maximal quotient ofC3×C49×Dic11⋊C5, C49×C3⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 2);