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C3×C5×AGL(1,𝔽5)×C41 #27134263

order12300
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×AGL(1,𝔽5)×C41

Splittings

Fitting, socle, HallC3×C52×C41 ⋊ C4
derivedC5 ⋊ C3×C4×C5×C41
HallC52×C41 ⋊ C3×C4
HallC3×C52 ⋊ C4×C41
SylowC52 ⋊ C3×C4×C41

Subgroups

subgroupG/H
center, hypercenterC3×C5×C41AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C5×C41
FrattiniC1G
Fitting, socleC3×C52×C41C4
prime radicalC3×C5×D5×C41C2
cosocleD5C2×C3×C5×C41
LCSG ▷ C5
UCSC1 ◁ C3×C5×C41

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3075 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×AGL(1,𝔽5)×C41, C32×C5×AGL(1,𝔽5)×C41, C3×C5×C41×ΓL(1,𝔽16)
maximal normal subgroup ofC5×C9×AGL(1,𝔽5)×C41, C32×C5×AGL(1,𝔽5)×C41
maximal quotient ofC5×C9×AGL(1,𝔽5)×C41, C32×C5×AGL(1,𝔽5)×C41, C3×C5×C41×ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 125);