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C5×C22⋊#87704 #22547740

order7980
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#87704
unambiguous semidirect productC22⋊(C5×#87704)
unambiguous semidirect product(C22×C5)⋊#87704

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C3
derived, HallC22×C7×C19 ⋊ C3×C5
HallC5×C7×C19 ⋊ A4
HallC22×C5×C19 ⋊ ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C19⋊C3
HallC7×C19 ⋊ C5×A4
HallC5×C19 ⋊ C22⋊ΓL(1,𝔽8)
HallC22×C19 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22⋊(C19⋊C3)
HallC22×C7 ⋊ C5×C19⋊C3
HallC22×C5 ⋊ #87704
SylowC19 ⋊ C5×C22⋊ΓL(1,𝔽8)
SylowC7 ⋊ C5×C22⋊(C19⋊C3)
SylowC22 ⋊ C5×#87704

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#87704
commutator, hypocenterC22×C7×C19C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C19C3
LCSG ▷ C22×C7×C19
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

900 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C19⋊C3×C22⋊ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×C22⋊(C19⋊C3), C5×A4×#87704, …
maximal normal subgroup ofC5×C19⋊C3×C22⋊ΓL(1,𝔽8), C5×ΓL(1,𝔽8)×C22⋊(C19⋊C3), C5×A4×#87704, …
maximal quotient ofC5×C22⋊#11924776, C3×C5×C22⋊#87704

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 165);