Finite Group Databasebeta

← Prev (#22547655) Next (#22547657) →

D5×#11716325 #22547656

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

Aliases

direct productD5×#11716325

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD5×D7×C19 ⋊ C3
HallC5×#87704 ⋊ C22
Hall#87704 ⋊ C2×D5
HallD5×D7 ⋊ C19⋊C3
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C22×C19⋊C3
SylowC19 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ C2×D5×C19⋊C3
SylowC5 ⋊ C2×#11716325

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

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽7)×C19⋊C3, C3×D5×#11716325, D15×#11716325, …
maximal normal subgroup ofD5×AGL(1,𝔽7)×C19⋊C3, C3×D5×#11716325
maximal quotient ofD5×#14558784, C3×D5×#11716325, D15×#11716325, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 81);