Finite Group Databasebeta

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C2×C19×C5⋊(D7⋊C9) #37560976

order23940
automorphism?
homologyAbelianization (H1) = C22×C9×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×C5⋊(D7⋊C9)
unambiguous semidirect product(C2×C5)⋊(C19×D7⋊C9)
unambiguous semidirect product(C2×C7⋊C9)⋊(D5×C19)
unambiguous semidirect product(C2×D35)⋊(C9×C19)

Splittings

derived, HallC5×C7 ⋊ C22×C9×C19
HallC5×C19×C7⋊C9 ⋊ C22
HallC2×C19×D35 ⋊ C9
HallC19×C7⋊C9 ⋊ C2×D5
HallC5×C7×C19 ⋊ C22×C9
HallC5×C7⋊C9 ⋊ C22×C19
HallC2×D35 ⋊ C9×C19
HallC7×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C2×D7⋊C9
HallC7⋊C9 ⋊ C2×D5×C19
SylowC7 ⋊ C2×C9×D5×C19
SylowC5 ⋊ C2×C19×D7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C22×C9×C19
FrattiniC3C2×C19×C5⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C19×D35C3
cosocleC3×C5×C7C22×C3×C19
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C19

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

1938 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 108);