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C2×C5×#11716325 #22547673

order7980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#11716325

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C3
derived, HallC7×C19 ⋊ C22×C3×C5
HallC2×C5×D7×C19 ⋊ C3
HallC5×#87704 ⋊ C22
HallC5×C7×C19 ⋊ C22×C3
HallC2×D7×C19 ⋊ C3×C5
Hall#87704 ⋊ C22×C5
HallC2×C5×D7 ⋊ C19⋊C3
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C19⋊C3
HallC2×D7 ⋊ C5×C19⋊C3
SylowC19 ⋊ C2×C5×AGL(1,𝔽7)
SylowC7 ⋊ C22×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#11716325
commutator, hypocenterC7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

370 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×AGL(1,𝔽7)×C19⋊C3, C5×D3×#11716325, C2×C3×C5×#11716325, …
maximal normal subgroup ofC2×C5×AGL(1,𝔽7)×C19⋊C3, C2×C3×C5×#11716325
maximal quotient ofC2×C5×#14558784, C5×D3×#11716325, C2×C3×C5×#11716325, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 98);