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C2×C5×C7×AGL(1,𝔽5) #13063846

order1400
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C4×C5×C7)

Splittings

Fitting, socleC2×C52×C7 ⋊ C4
derivedC5 ⋊ C2×C4×C5×C7
HallC52×C7 ⋊ C2×C4
SylowC52 ⋊ C2×C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽5)
commutator, hypocenterC5C2×C4×C5×C7
FrattiniC1G
Fitting, socleC2×C52×C7C4
prime radicalC2×C5×C7×D5C2
cosocleD5C22×C5×C7
LCSG ▷ C5
UCSC1 ◁ C2×C5×C7

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 280

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5×AGL(1,𝔽5)×ΓL(1,𝔽8), C2×C5×D7×AGL(1,𝔽5), C4×C5×C7×AGL(1,𝔽5), …
maximal normal subgroup ofC2×C5×AGL(1,𝔽5)×ΓL(1,𝔽8), C2×C5×D7×AGL(1,𝔽5), C4×C5×C7×AGL(1,𝔽5), …
maximal quotient ofC4×C5×C7×AGL(1,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 135);