Finite Group Databasebeta

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C5×C7×D5×AGL(1,𝔽7) #28413232

order14700
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×D5×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C5×C7×D5)
unambiguous semidirect product(D5×D7)⋊(C3×C5×C7)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊(C2×C5×C7)
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊(C2×C5×C7)
unambiguous semidirect product(C5⋊AGL(1,𝔽7))⋊(C2×C5×C7)
unambiguous semidirect product(C5×D5×D7)⋊(C3×C7)

Splittings

Fitting, socle, HallC52×C72 ⋊ C22×C3
derivedC5×C7 ⋊ C22×C3×C5×C7
HallC5×C7×D5×D7 ⋊ C3
HallC52×C7×ΓL(1,𝔽8) ⋊ C22
HallC7×ΓL(1,𝔽8) ⋊ C2×C5×D5
SylowC72 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C2×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC5×C7D5×AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C3×C5×C7
FrattiniC1G
Fitting, socleC52×C72C22×C3
LCSG ▷ C5×C7
UCSC1 ◁ C5×C7

202 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 411);