Finite Group Databasebeta

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C3×A4×C25×C37 #45685924

order33300
automorphism?
homologyAbelianization (H1) = C32×C25×C37 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C25×C37
unambiguous semidirect productC22⋊(C32×C25×C37)
unambiguous semidirect product(C22×C3)⋊(C3×C25×C37)
unambiguous semidirect product(C22×C25)⋊(C32×C37)
unambiguous semidirect product(C22×C3×C25)⋊(C3×C37)

Splittings

FittingC22×C3×C25×C37 ⋊ C3
derived, SylowC22 ⋊ C32×C25×C37
HallC22×C25×C37 ⋊ C32
HallC22×C37 ⋊ C32×C25
HallC22×C25 ⋊ C32×C37

Subgroups

subgroupG/H
center, hypercenterC3×C25×C37A4
commutator, hypocenterC22C32×C25×C37
FrattiniC5C3×C5×A4×C37
FittingC22×C3×C25×C37C3
socleC22×C3×C5×C37C3×C5
prime radicalC3×C5×A4×C37C5
cosocleC22×C5C32×C5×C37
LCSG ▷ C22
UCSC1 ◁ C3×C25×C37

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11100

Conjugacy classes & character table

11100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 197);