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C5×C11×C49⋊C3 #22549111

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

Aliases

direct productC5×C11×C49⋊C3
unambiguous semidirect productC49⋊(C3×C5×C11)
unambiguous semidirect product(C5×C49)⋊(C3×C11)
unambiguous semidirect product(C5×C11×C49)⋊C3

Splittings

Fitting, HallC5×C11×C49 ⋊ C3
derived, SylowC49 ⋊ C3×C5×C11
HallC11×C49 ⋊ C3×C5
HallC5×C49 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11C49⋊C3
commutator, hypocenterC49C3×C5×C11
FrattiniC7C5×C11×ΓL(1,𝔽8)
FittingC5×C11×C49C3
socleC5×C7×C11ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C5×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1045 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×C49⋊C3, C5×D11×C49⋊C3, C5×C11×D49⋊C3, …
maximal normal subgroup ofC2×C5×C11×C49⋊C3, C5×D11×C49⋊C3, C5×C11×D49⋊C3, …
maximal quotient ofC2×C5×C11×C49⋊C3, C5×C11×C49⋊C9, C3×C5×C11×C49⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8085, 4);