Finite Group Databasebeta

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C5×C22⋊#11924780 #37561424

order23940
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#11924780
unambiguous semidirect productC22⋊(C5×#11924780)
unambiguous semidirect product(C22×C5)⋊#11924780

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C9
derived, HallC22×C7×C19 ⋊ C5×C9
HallC5×C7×C19 ⋊ C22⋊C9
HallC22×C5×C19 ⋊ C7⋊C9
HallC22×C5×C7 ⋊ #4296
HallC7×C19 ⋊ C5×C22⋊C9
HallC5×C19 ⋊ C22⋊(C7⋊C9)
HallC22×C19 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C22⋊#4296
HallC22×C7 ⋊ C5×#4296
HallC22×C5 ⋊ #11924780
SylowC19 ⋊ C5×C22⋊(C7⋊C9)
SylowC7 ⋊ C5×C22⋊#4296
SylowC22 ⋊ C5×#11924780

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#11924780
commutator, hypocenterC22×C7×C19C5×C9
FrattiniC1G
Fitting, socleC22×C5×C7×C19C9
prime radicalC22×C5×C7×C19⋊C3C3
cosocleC22×C7×C19⋊C3C3×C5
LCSG ▷ C22×C7×C19
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 556);