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D5×#11716328 #22547653

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

Aliases

direct productD5×#11716328

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD5×D133 ⋊ C3
HallC5×#87705 ⋊ C22
Hall#87705 ⋊ C2×D5
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D19⋊C3
SylowC19 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ D5×D19⋊C3
SylowC5 ⋊ C2×#11716328

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)⋊(D19⋊C3), C3×D5×#11716328, D15×#11716328, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)⋊(D19⋊C3), C3×D5×#11716328
maximal quotient ofD5×#14558787, C3×D5×#11716328, D15×#11716328, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 78);