Finite Group Databasebeta

← Prev (#44530435) Next (#44530437) →

C3×C4×C521⋊C5 #44530436

order31260
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C521⋊C5
unambiguous semidirect product(C4×C521)⋊(C3×C5)
unambiguous semidirect product(C3×C4×C521)⋊C5

Splittings

Fitting, HallC3×C4×C521 ⋊ C5
derived, SylowC521 ⋊ C3×C4×C5
HallC4×C521 ⋊ C3×C5
HallC3×C521 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C521⋊C5
commutator, hypocenterC521C3×C4×C5
FrattiniC2C2×C3×C521⋊C5
FittingC3×C4×C521C5
socleC2×C3×C521C2×C5
prime radicalC2×C3×C521⋊C5C2
cosocleC2×C521C2×C3×C5
LCSG ▷ C521
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6252

Conjugacy classes & character table

1308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31260, 2);