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A4×C25×C41 #27134179

order12300
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C25×C41 · Schur multiplier (H2) = C2

Aliases

direct productA4×C25×C41
unambiguous semidirect productC22⋊(C3×C25×C41)
unambiguous semidirect product(C22×C25)⋊(C3×C41)
unambiguous semidirect product(C22×C25×C41)⋊C3

Splittings

Fitting, HallC22×C25×C41 ⋊ C3
derived, SylowC22 ⋊ C3×C25×C41
HallC22×C41 ⋊ C3×C25
HallC22×C25 ⋊ C3×C41

Subgroups

subgroupG/H
center, hypercenterC25×C41A4
commutator, hypocenterC22C3×C25×C41
FrattiniC5C5×A4×C41
FittingC22×C25×C41C3
socleC22×C5×C41C3×C5
prime radicalC5×A4×C41C5
cosocleC22×C5C3×C5×C41
LCSG ▷ C22
UCSC1 ◁ C25×C41

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×A4×C25×C41
maximal normal subgroup ofC3×A4×C25×C41
maximal quotient ofC25×C22⋊C9×C41, C3×A4×C25×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 41);