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C22×C17×C41⋊C5 #28358289

order13940
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC22×C17×C41⋊C5
unambiguous semidirect product(C22×C41)⋊(C5×C17)
unambiguous semidirect product(C22×C17×C41)⋊C5

Splittings

Fitting, socle, HallC22×C17×C41 ⋊ C5
derived, SylowC41 ⋊ C22×C5×C17
HallC17×C41 ⋊ C22×C5
HallC22×C41 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC22×C17C41⋊C5
commutator, cosocle, hypocenterC41C22×C5×C17
FrattiniC1G
Fitting, socleC22×C17×C41C5
LCSG ▷ C41
UCSC1 ◁ C22×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2788

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13940, 24);