Finite Group Databasebeta

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C3×A4×C23×C25 #35207979

order20700
automorphism?
homologyAbelianization (H1) = C32×C23×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C23×C25
unambiguous semidirect productC22⋊(C32×C23×C25)
unambiguous semidirect product(C22×C3)⋊(C3×C23×C25)
unambiguous semidirect product(C22×C23)⋊(C32×C25)
unambiguous semidirect product(C22×C25)⋊(C32×C23)
unambiguous semidirect product(C22×C3×C23)⋊(C3×C25)
unambiguous semidirect product(C22×C3×C25)⋊(C3×C23)
unambiguous semidirect product(C22×C23×C25)⋊C32
unambiguous semidirect product(C22×C3×C23×C25)⋊C3

Splittings

FittingC22×C3×C23×C25 ⋊ C3
derived, SylowC22 ⋊ C32×C23×C25
HallC22×C23×C25 ⋊ C32
HallC22×C25 ⋊ C32×C23
HallC22×C23 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC3×C23×C25A4
commutator, hypocenterC22C32×C23×C25
FrattiniC5C3×C5×A4×C23
FittingC22×C3×C23×C25C3
socleC22×C3×C5×C23C3×C5
prime radicalC3×C5×A4×C23C5
cosocleC22×C5C32×C5×C23
LCSG ▷ C22
UCSC1 ◁ C3×C23×C25

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6900

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 95);