Finite Group Databasebeta

← Prev (#22547639) Next (#22547641) →

AGL(1,𝔽5)×#87704 #22547640

order7980
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×#87704

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C3×C4
HallC7×C19×AGL(1,𝔽5) ⋊ C3
HallC5×#87704 ⋊ C4
HallC19×AGL(1,𝔽5) ⋊ ΓL(1,𝔽8)
HallC7×AGL(1,𝔽5) ⋊ C19⋊C3
HallC7×C19 ⋊ C3×AGL(1,𝔽5)
HallC5×C19 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C19⋊C3
SylowC19 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ AGL(1,𝔽5)×C19⋊C3
SylowC5 ⋊ C4×#87704

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C3×C4
LCSG ▷ C5×C7×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C19⋊C3, C3×AGL(1,𝔽5)×#87704, ΓL(1,𝔽16)×#87704
maximal normal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)×C19⋊C3, C3×AGL(1,𝔽5)×#87704
maximal quotient ofAGL(1,𝔽5)×#11924776, C3×AGL(1,𝔽5)×#87704, ΓL(1,𝔽16)×#87704

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 65);