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C22×C13×C41⋊C5 #24922506

order10660
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13×C41⋊C5
unambiguous semidirect product(C22×C41)⋊(C5×C13)
unambiguous semidirect product(C22×C13×C41)⋊C5

Splittings

Fitting, socle, HallC22×C13×C41 ⋊ C5
derived, SylowC41 ⋊ C22×C5×C13
HallC13×C41 ⋊ C22×C5
HallC22×C41 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC22×C13C41⋊C5
commutator, cosocle, hypocenterC41C22×C5×C13
FrattiniC1G
Fitting, socleC22×C13×C41C5
LCSG ▷ C41
UCSC1 ◁ C22×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C13×C41⋊C5, C22⋊(C13⋊C3)×C41⋊C5, C22×C13⋊C3×C41⋊C5, …
maximal normal subgroup ofA4×C13×C41⋊C5, C22⋊(C13⋊C3)×C41⋊C5, C22×C13⋊C3×C41⋊C5, …
maximal quotient ofC2×D3×C13×C41⋊C5, C22×C3×C13×C41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10660, 24);