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C4×C49×C11⋊C5 #24924692

order10780
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC4×C49×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C49)
unambiguous semidirect product(C4×C11×C49)⋊C5

Splittings

Fitting, HallC4×C11×C49 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C49
HallC11×C49 ⋊ C4×C5
HallC4×C11 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC4×C49C11⋊C5
commutator, hypocenterC11C4×C5×C49
FrattiniC2×C7C2×C7×C11⋊C5
FittingC4×C11×C49C5
socle, cosocleC2×C7×C11C2×C5×C7
prime radicalC2×C7×C11⋊C5C2×C7
LCSG ▷ C11
UCSC1 ◁ C4×C49

36 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 ofC3×C4×C49×C11⋊C5, C4×C11⋊C5×C49⋊C3, Dic3×C49×C11⋊C5
maximal normal subgroup ofC3×C4×C49×C11⋊C5, C4×C11⋊C5×C49⋊C3
maximal quotient ofC3×C4×C49×C11⋊C5, Dic3×C49×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 5);