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C2×C5⋊#11716321 #22547690

order7980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊#11716321
unambiguous semidirect product(C2×C5)⋊#11716321

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C22×C3
HallC2×C7×D95 ⋊ C3
HallC5×#87704 ⋊ C22
Hall#87704 ⋊ C2×D5
HallC2×D95 ⋊ ΓL(1,𝔽8)
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C22×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C5⋊(D19⋊C3)
SylowC5 ⋊ C2×#11716321

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#11716321
commutator, hypocenterC5×C7×C19C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×C5⋊(D19⋊C3), D3×C5⋊#11716321, C2×C3×C5⋊#11716321, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×C5⋊(D19⋊C3), C2×C3×C5⋊#11716321
maximal quotient ofC2×C5⋊#14558780, D3×C5⋊#11716321, C2×C3×C5⋊#11716321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 115);