Finite Group Databasebeta

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C2×D5×#11924780 #37561244

order23940
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×#11924780
unambiguous semidirect productC5⋊(C22×#11924780)
unambiguous semidirect product(C2×C5)⋊(C2×#11924780)

Splittings

Fitting, socleC2×C5×C7×C19 ⋊ C2×C9
derived, HallC5×C7×C19 ⋊ C22×C9
HallC5×#11924780 ⋊ C22
HallC2×C7×D5×C19 ⋊ C9
HallC2×D5×C19 ⋊ C7⋊C9
HallC2×C7×D5 ⋊ #4296
HallC7×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C22×C7⋊C9
HallC5×C7 ⋊ C22×#4296
SylowC19 ⋊ C2×D5×C7⋊C9
SylowC7 ⋊ C2×D5×#4296
SylowC5 ⋊ C22×#11924780

Subgroups

subgroupG/H
center, hypercenterC2D5×#11924780
commutator, hypocenterC5×C7×C19C22×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C19C2×C9
prime radicalC2×C7×D5×C19⋊C3C3
cosocleC5×C7×C19⋊C3C22×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1330

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 376);