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AGL(1,𝔽5)×#92788 #23778482

order10140
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×#92788

Splittings

Fitting, socle, derived, HallC5×C132 ⋊ C3×C4
HallC132×AGL(1,𝔽5) ⋊ C3
HallC5×#92788 ⋊ C4
SylowC132 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ C4×#92788

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C132C3×C4
prime radicalD5×#92788C2
cosocleD5×C132C2×C3
LCSG ▷ C5×C132
UCSC1

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

295 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C13⋊C32, C3×AGL(1,𝔽5)×#92788, ΓL(1,𝔽16)×#92788
maximal normal subgroup ofAGL(1,𝔽5)×C13⋊C32, C3×AGL(1,𝔽5)×#92788
maximal quotient ofAGL(1,𝔽5)×#13095200, C3×AGL(1,𝔽5)×#92788, ΓL(1,𝔽16)×#92788

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 140);