Finite Group Databasebeta

← Prev (#14523536) Next (#14523538) →

C2×C25×AGL(1,𝔽7) #14523537

order2100
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C25)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C25)
unambiguous semidirect product(C2×D7)⋊(C3×C25)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C25)
unambiguous semidirect product(C2×D7×C25)⋊C3

Splittings

FittingC2×C7×C25 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C25
HallC2×D7×C25 ⋊ C3
HallΓL(1,𝔽8)×C25 ⋊ C22
HallC7×C25 ⋊ C22×C3
HallC2×D7 ⋊ C3×C25
HallΓL(1,𝔽8) ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C25
FrattiniC5C2×C5×AGL(1,𝔽7)
FittingC2×C7×C25C2×C3
socleC2×C5×C7C2×C3×C5
prime radicalC2×C5×AGL(1,𝔽7)C5
cosocleC5×C7C22×C3×C5
LCSG ▷ C7
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 350

Conjugacy classes & character table

350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C25×D49⋊C3, C25×#64423⋊C2, C25×#64422⋊C2, …
maximal normal subgroup ofC2×C7×C25×AGL(1,𝔽7), C2×C11×C25×AGL(1,𝔽7), C2×C13×C25×AGL(1,𝔽7), …
maximal quotient ofC2×C25×D49⋊C3, C25×#64423⋊C2, C25×#64422⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 17);