Finite Group Databasebeta

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C5×A4×C529 #44540683

order31740
automorphism?
homologyAbelianization (H1) = C3×C5×C529 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C529
unambiguous semidirect productC22⋊(C3×C5×C529)
unambiguous semidirect product(C22×C5)⋊(C3×C529)
unambiguous semidirect product(C22×C529)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C529)⋊C3

Splittings

Fitting, HallC22×C5×C529 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C529
HallC22×C529 ⋊ C3×C5
HallC22×C5 ⋊ C3×C529

Subgroups

subgroupG/H
center, hypercenterC5×C529A4
commutator, hypocenterC22C3×C5×C529
FrattiniC23C5×A4×C23
FittingC22×C5×C529C3
socleC22×C5×C23C3×C23
prime radicalC5×A4×C23C23
cosocleC22×C23C3×C5×C23
LCSG ▷ C22
UCSC1 ◁ C5×C529

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10580

Conjugacy classes & character table

10580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 21);