Finite Group Databasebeta

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C5×A4×C361 #36343108

order21660
automorphism?
homologyAbelianization (H1) = C3×C5×C361 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C361
unambiguous semidirect productC22⋊(C3×C5×C361)
unambiguous semidirect product(C22×C5)⋊(C3×C361)

Splittings

Fitting, HallC22×C5×C361 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C361
HallC22×C361 ⋊ C3×C5
HallC22×C5 ⋊ C3×C361

Subgroups

subgroupG/H
center, hypercenterC5×C361A4
commutator, hypocenterC22C3×C5×C361
FrattiniC19C5×A4×C19
FittingC22×C5×C361C3
socleC22×C5×C19C3×C19
prime radicalC5×A4×C19C19
cosocleC22×C19C3×C5×C19
LCSG ▷ C22
UCSC1 ◁ C5×C361

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7220

Conjugacy classes & character table

7220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 32);