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C41×C3⋊#1035 #27134169

order12300
isoclinismisoclinic class of C3⋊#1035
automorphism?
homologyAbelianization (H1) = C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC41×C3⋊#1035
unambiguous semidirect productC3⋊(C41×#1035)

Splittings

Fitting, HallC3×C25×C41 ⋊ C4
derived, HallC3×C25 ⋊ C4×C41
HallC25×C41 ⋊ Dic3
HallC3×C41 ⋊ #1035
SylowC25 ⋊ Dic3×C41
SylowC3 ⋊ C41×#1035

Subgroups

subgroupG/H
center, hypercenterC41C3⋊#1035
commutator, hypocenterC3×C25C4×C41
FrattiniC5C41×ΓL(1,𝔽16)
FittingC3×C25×C41C4
socleC3×C5×C41AGL(1,𝔽5)
prime radicalC3×C41×D25C2
cosocleC3×D25C2×C41
LCSG ▷ C3×C25
UCSC1 ◁ C41

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

984 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×C9⋊#1035, C3×C41×C3⋊#1035, C41×C3⋊(C3⋊#1035)
maximal normal subgroup ofC3×C41×C3⋊#1035
maximal quotient ofC41×C9⋊#1035, C3×C41×C3⋊#1035, C41×C3⋊(C3⋊#1035)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 31);