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C32×#4223⋊C5 #20301590

order7380
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×#4223⋊C5
unambiguous semidirect product#4223⋊(C32×C5)
unambiguous semidirect product(C3×#4223)⋊(C3×C5)
unambiguous semidirect product(C32×#4223)⋊C5

Splittings

Fitting, socle, HallC32×C41 ⋊ C4×C5
derived, SylowC41 ⋊ C32×C4×C5
HallC32×C41⋊C5 ⋊ C4
HallC32×#4223 ⋊ C5
HallC41⋊C5 ⋊ C32×C4
Hall#4223 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32#4223⋊C5
commutator, hypocenterC41C32×C4×C5
FrattiniC1G
Fitting, socleC32×C41C4×C5
LCSG ▷ C41
UCSC1 ◁ C32

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×C5×#4223⋊C5, C32×#11717961⋊C5, C32×#11717962⋊C5, …
maximal normal subgroup ofC32×C5×#4223⋊C5, C3⋊D3×#4223⋊C5, C32×AGL(1,𝔽41), …
maximal quotient ofC32×#4223⋊C25, C32×C5×#4223⋊C5, C32×#11717961⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 68);