Finite Group Databasebeta

← Prev (#14523598) Next (#14523600) →

AGL(1,𝔽7)×C5⋊D5 #14523599

order2100
isoclinismisoclinic class of AGL(1,𝔽7)×C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productAGL(1,𝔽7)×C5⋊D5
unambiguous semidirect productD7⋊(C3×C5⋊D5)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊D5

Splittings

Fitting, socle, derived, HallC52×C7 ⋊ C22×C3
HallD7×C5⋊D5 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C22
SylowC52 ⋊ C2×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C5⋊D5
SylowC7 ⋊ C2×C3×C5⋊D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7C22×C3
LCSG ▷ C52×C7
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 175

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5⋊D5×D49⋊C3, C7×AGL(1,𝔽7)×C5⋊D5, C5⋊D5×#64424, …
maximal normal subgroup ofC7×AGL(1,𝔽7)×C5⋊D5, C11×AGL(1,𝔽7)×C5⋊D5, C13×AGL(1,𝔽7)×C5⋊D5, …
maximal quotient ofC5⋊D5×D49⋊C3, C7×AGL(1,𝔽7)×C5⋊D5, C5⋊D5×#64424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 79);