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C22×C3×C5×AGL(1,𝔽5) #11925807

order1200
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC22×C3×C5×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C2×C3×C4×C5)

Splittings

Fitting, socleC22×C3×C52 ⋊ C4
derivedC5 ⋊ C22×C3×C4×C5
HallC3×C52 ⋊ C22×C4
SylowC52 ⋊ C22×C3×C4

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5AGL(1,𝔽5)
commutator, hypocenterC5C22×C3×C4×C5
FrattiniC1G
Fitting, socleC22×C3×C52C4
prime radicalC22×C3×C5×D5C2
cosocleD5C23×C3×C5
LCSG ▷ C5
UCSC1 ◁ C22×C3×C5

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×C3×AGL(1,ℤ/25), C2×C3×C4×C5×AGL(1,𝔽5), C2×C5×AGL(1,𝔽5)×AGL(1,𝔽7), …
maximal normal subgroup ofC2×C3×C4×C5×AGL(1,𝔽5), C22×C32×C5×AGL(1,𝔽5), C22×C5×D3×AGL(1,𝔽5), …
maximal quotient ofC22×C3×AGL(1,ℤ/25), C2×C3×C4×C5×AGL(1,𝔽5), C2×C5×AGL(1,𝔽5)×AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 1017);