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C2×C3×C11×D41 #19129295

order5412
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D41
unambiguous semidirect productC41⋊(C22×C3×C11)
unambiguous semidirect product(C2×C41)⋊(C2×C3×C11)

Splittings

Fitting, socleC2×C3×C11×C41 ⋊ C2
derived, SylowC41 ⋊ C22×C3×C11
HallC3×C11×C41 ⋊ C22
HallC11×C41 ⋊ C22×C3
HallC3×C41 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D41
commutator, hypocenterC41C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C41C2
LCSG ▷ C41
UCSC1 ◁ C2×C3×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1452 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C9×C11×D41, C3×D3×C11×D41, C2×C3×C11×D123, …
maximal normal subgroup ofC2×C9×C11×D41, C2×C32×C11×D41, C2×C3×C11×D41⋊C5, …
maximal quotient ofC2×C9×C11×D41, C3×D3×C11×D41, C2×C3×C11×D123, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5412, 28);